Ideal-Gas Processes 21st July 2014 - Physics &...
Transcript of Ideal-Gas Processes 21st July 2014 - Physics &...
![Page 1: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/1.jpg)
July 21, Week 8
Ideal-Gas Processes 21st July 2014
Today: Ideal-Gas Processes, Chapter 12
Final Homework #7 due today at 5:00. Office hours, 1:00-5:00
Final Exam, Thursday. 9:00-10:30 or 11:00-12:15
![Page 2: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/2.jpg)
Pressure
Ideal-Gas Processes 21st July 2014
When the molecules in a gas or liquid collide with its container, theyexert a force on the container
![Page 3: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/3.jpg)
Pressure
Ideal-Gas Processes 21st July 2014
When the molecules in a gas or liquid collide with its container, theyexert a force on the container
![Page 4: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/4.jpg)
Pressure
Ideal-Gas Processes 21st July 2014
When the molecules in a gas or liquid collide with its container, theyexert a force on the container
Collisions cause an outward forceover the entirety of the container’ssurface area
![Page 5: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/5.jpg)
Pressure
Ideal-Gas Processes 21st July 2014
When the molecules in a gas or liquid collide with its container, theyexert a force on the container
Collisions cause an outward forceover the entirety of the container’ssurface area
Pressure = “average” force per area
p =F
Aunit: N/m2 = Pa (Pascal)
![Page 6: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/6.jpg)
Pressure
Ideal-Gas Processes 21st July 2014
When the molecules in a gas or liquid collide with its container, theyexert a force on the container
Collisions cause an outward forceover the entirety of the container’ssurface area
Pressure = “average” force per area
p =F
Aunit: N/m2 = Pa (Pascal)
Other pressure units: atmospheres (atm), millimeters of mercury(mmHg = torr), and pounds per square inch (psi)
![Page 7: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/7.jpg)
Pressure
Ideal-Gas Processes 21st July 2014
When the molecules in a gas or liquid collide with its container, theyexert a force on the container
Collisions cause an outward forceover the entirety of the container’ssurface area
Pressure = “average” force per area
p =F
Aunit: N/m2 = Pa (Pascal)
Other pressure units: atmospheres (atm), millimeters of mercury(mmHg = torr), and pounds per square inch (psi)
1 atm = 101300Pa = 101.3 kPa = 760mmHg = 14.7 psi
![Page 8: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/8.jpg)
The Ideal-Gas Equation
Ideal-Gas Processes 21st July 2014
In an ideal gas, the relationship between the pressure (p), volume(V ) and temperature (T ) of the gas is given by:
![Page 9: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/9.jpg)
The Ideal-Gas Equation
Ideal-Gas Processes 21st July 2014
In an ideal gas, the relationship between the pressure (p), volume(V ) and temperature (T ) of the gas is given by:
pV = NkBTN = number of molecules
kB = 1.38× 10−23 J/K = Boltzmann’s constant
![Page 10: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/10.jpg)
The Ideal-Gas Equation
Ideal-Gas Processes 21st July 2014
In an ideal gas, the relationship between the pressure (p), volume(V ) and temperature (T ) of the gas is given by:
pV = NkBTN = number of molecules
kB = 1.38× 10−23 J/K = Boltzmann’s constant
If forced to use moles:
![Page 11: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/11.jpg)
The Ideal-Gas Equation
Ideal-Gas Processes 21st July 2014
In an ideal gas, the relationship between the pressure (p), volume(V ) and temperature (T ) of the gas is given by:
pV = NkBTN = number of molecules
kB = 1.38× 10−23 J/K = Boltzmann’s constant
If forced to use moles: n = number of moles: N = n×NA
Avogadro’s Number: NA = 6.02× 1023
![Page 12: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/12.jpg)
The Ideal-Gas Equation
Ideal-Gas Processes 21st July 2014
In an ideal gas, the relationship between the pressure (p), volume(V ) and temperature (T ) of the gas is given by:
pV = NkBTN = number of molecules
kB = 1.38× 10−23 J/K = Boltzmann’s constant
If forced to use moles: n = number of moles: N = n×NA
Avogadro’s Number: NA = 6.02× 1023
pV = nRT R = kB ×NA = 8.31 J/mole ·K
![Page 13: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/13.jpg)
The Ideal-Gas Equation
Ideal-Gas Processes 21st July 2014
In an ideal gas, the relationship between the pressure (p), volume(V ) and temperature (T ) of the gas is given by:
pV = NkBTN = number of molecules
kB = 1.38× 10−23 J/K = Boltzmann’s constant
If forced to use moles: n = number of moles: N = n×NA
Avogadro’s Number: NA = 6.02× 1023
pV = nRT R = kB ×NA = 8.31 J/mole ·K
When a gas is in a sealed container, the total number of particles mustremain constant
![Page 14: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/14.jpg)
The Ideal-Gas Equation
Ideal-Gas Processes 21st July 2014
In an ideal gas, the relationship between the pressure (p), volume(V ) and temperature (T ) of the gas is given by:
pV = NkBTN = number of molecules
kB = 1.38× 10−23 J/K = Boltzmann’s constant
If forced to use moles: n = number of moles: N = n×NA
Avogadro’s Number: NA = 6.02× 1023
pV = nRT R = kB ×NA = 8.31 J/mole ·K
When a gas is in a sealed container, the total number of particles mustremain constant
pV
T= NkB = constant ⇒
piVi
Ti
=pfVf
Tf
![Page 15: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/15.jpg)
Ideal-Gas Exercise I
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half, bywhat ratio does the temperature change?
Moveable Piston
![Page 16: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/16.jpg)
Ideal-Gas Exercise I
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half, bywhat ratio does the temperature change?
Moveable Piston
![Page 17: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/17.jpg)
Ideal-Gas Exercise I
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half, bywhat ratio does the temperature change?
Moveable Piston
(a) The temperature will double.
![Page 18: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/18.jpg)
Ideal-Gas Exercise I
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half, bywhat ratio does the temperature change?
Moveable Piston
(a) The temperature will double.
(b) The temperature will stay the same.
![Page 19: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/19.jpg)
Ideal-Gas Exercise I
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half, bywhat ratio does the temperature change?
Moveable Piston
(a) The temperature will double.
(b) The temperature will stay the same.
(c) The temperature will be cut in half.
![Page 20: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/20.jpg)
Ideal-Gas Exercise I
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half, bywhat ratio does the temperature change?
Moveable Piston
(a) The temperature will double.
(b) The temperature will stay the same.
(c) The temperature will be cut in half.
(d) There is not enough information todetermine.
![Page 21: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/21.jpg)
Ideal-Gas Exercise I
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half, bywhat ratio does the temperature change?
Moveable Piston
(a) The temperature will double.
(b) The temperature will stay the same.
(c) The temperature will be cut in half.
(d) There is not enough information todetermine.
(e) Intentionally left blank.
![Page 22: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/22.jpg)
Ideal-Gas Exercise I
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half, bywhat ratio does the temperature change?
Moveable Piston
(a) The temperature will double.
(b) The temperature will stay the same.
(c) The temperature will be cut in half.
(d) There is not enough information todetermine.
(e) Intentionally left blank.
![Page 23: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/23.jpg)
Ideal-Gas Exercise I
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half, bywhat ratio does the temperature change?
Moveable Piston
(d) There is not enough information todetermine.
Even when N is fixed, pV = nkBT is a function of three variables: p, Vand T . In order to figure out how one of them is changing, we need toknow something about the other two.
![Page 24: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/24.jpg)
Ideal-Gas Exercise II
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half whilethe pressure is kept constant, by what ratio does the temperaturechange?
Moveable Piston
![Page 25: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/25.jpg)
Ideal-Gas Exercise II
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half whilethe pressure is kept constant, by what ratio does the temperaturechange?
Moveable Piston
![Page 26: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/26.jpg)
Ideal-Gas Exercise II
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half whilethe pressure is kept constant, by what ratio does the temperaturechange?
Moveable Piston
(a) The temperature will double.
![Page 27: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/27.jpg)
Ideal-Gas Exercise II
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half whilethe pressure is kept constant, by what ratio does the temperaturechange?
Moveable Piston
(a) The temperature will double.
(b) The temperature will stay the same.
![Page 28: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/28.jpg)
Ideal-Gas Exercise II
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half whilethe pressure is kept constant, by what ratio does the temperaturechange?
Moveable Piston
(a) The temperature will double.
(b) The temperature will stay the same.
(c) The temperature will be cut in half.
![Page 29: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/29.jpg)
Ideal-Gas Exercise II
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half whilethe pressure is kept constant, by what ratio does the temperaturechange?
Moveable Piston
(a) The temperature will double.
(b) The temperature will stay the same.
(c) The temperature will be cut in half.
(d) There is not enough information todetermine.
![Page 30: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/30.jpg)
Ideal-Gas Exercise II
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half whilethe pressure is kept constant, by what ratio does the temperaturechange?
Moveable Piston
(a) The temperature will double.
(b) The temperature will stay the same.
(c) The temperature will be cut in half.
(d) There is not enough information todetermine.
(e) Intentionally left blank.
![Page 31: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/31.jpg)
Ideal-Gas Exercise II
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half whilethe pressure is kept constant, by what ratio does the temperaturechange?
Moveable Piston
(a) The temperature will double.
(b) The temperature will stay the same.
(c) The temperature will be cut in half.
(d) There is not enough information todetermine.
(e) Intentionally left blank.
![Page 32: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/32.jpg)
Ideal-Gas Exercise II
Ideal-Gas Processes 21st July 2014
A gas is sealed in a container that has a moveable piston on oneside (so the volume can change). If the volume is cut in half whilethe pressure is kept constant, by what ratio does the temperaturechange?
Moveable Piston(c) The temperature will be cut in half.
With N and p are fixed, V =NkBp
T ⇒ V = constant× T ⇒ cutting V
in half, cuts T in half.
![Page 33: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/33.jpg)
Work done by a Gas
Ideal-Gas Processes 21st July 2014
Volume changes occur when the gas exerts a large enough forceon its container to move it by some distance
![Page 34: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/34.jpg)
Work done by a Gas
Ideal-Gas Processes 21st July 2014
Volume changes occur when the gas exerts a large enough forceon its container to move it by some distance
Initial−→
Fgas−→
Fext
![Page 35: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/35.jpg)
Work done by a Gas
Ideal-Gas Processes 21st July 2014
Volume changes occur when the gas exerts a large enough forceon its container to move it by some distance
Initial−→
Fgas−→
Fext
Final−→
Fgas−→
Fext
![Page 36: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/36.jpg)
Work done by a Gas
Ideal-Gas Processes 21st July 2014
Volume changes occur when the gas exerts a large enough forceon its container to move it by some distance
Initial−→
Fgas−→
Fext
Final−→
Fgas−→
Fext
For a constant force: W = Fd
d
![Page 37: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/37.jpg)
Work done by a Gas
Ideal-Gas Processes 21st July 2014
Volume changes occur when the gas exerts a large enough forceon its container to move it by some distance
Initial−→
Fgas−→
Fext
Final−→
Fgas−→
Fext
For a constant force: W = Fd
dWgas =
(
Fgas
A
)
(dA)
Area = A
![Page 38: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/38.jpg)
Work done by a Gas
Ideal-Gas Processes 21st July 2014
Volume changes occur when the gas exerts a large enough forceon its container to move it by some distance
Initial−→
Fgas−→
Fext
Final−→
Fgas−→
Fext
For a constant force: W = Fd
dWgas =
(
Fgas
A
)
(dA)
Area = A
Wgas = p∆V Constant Pressure
![Page 39: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/39.jpg)
Work done by a Gas
Ideal-Gas Processes 21st July 2014
Volume changes occur when the gas exerts a large enough forceon its container to move it by some distance
Initial−→
Fgas−→
Fext
Final−→
Fgas−→
Fext
For a constant force: W = Fd
dWgas =
(
Fgas
A
)
(dA)
Area = A
Wgas = p∆V Constant Pressure
V
p i
f
When pressure changes,we use a “pV diagram ⇒
pressure on the y-axis andvolume on the x-axis.
![Page 40: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/40.jpg)
Work done by a Gas
Ideal-Gas Processes 21st July 2014
Volume changes occur when the gas exerts a large enough forceon its container to move it by some distance
Initial−→
Fgas−→
Fext
Final−→
Fgas−→
Fext
For a constant force: W = Fd
dWgas =
(
Fgas
A
)
(dA)
Area = A
Wgas = p∆V Constant Pressure
V
p i
f
Wgas is the area under thepV diagramWhen pressure changes,
we use a “pV diagram ⇒
pressure on the y-axis andvolume on the x-axis.
![Page 41: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/41.jpg)
Processes Exercise I
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isobaric =constant pressure process?
![Page 42: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/42.jpg)
Processes Exercise I
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isobaric =constant pressure process?
(a)
V
p i f
![Page 43: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/43.jpg)
Processes Exercise I
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isobaric =constant pressure process?
(a)
V
p i f
(b)
V
p i
f
![Page 44: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/44.jpg)
Processes Exercise I
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isobaric =constant pressure process?
(a)
V
p i f
(b)
V
p i
f
(c)
V
p i
f
![Page 45: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/45.jpg)
Processes Exercise I
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isobaric =constant pressure process?
(a)
V
p i f
(b)
V
p i
f
(c)
V
p i
f
(d)
V
p i
f
![Page 46: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/46.jpg)
Processes Exercise I
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isobaric =constant pressure process?
(a)
V
p i f
(b)
V
p i
f
(c)
V
p i
f
(d)
V
p i
f
(e) Intentionallyleft blank
![Page 47: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/47.jpg)
Processes Exercise I
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isobaric =constant pressure process?
(a)
V
p i f
(b)
V
p i
f
(c)
V
p i
f
(d)
V
p i
f
(e) Intentionallyleft blank
![Page 48: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/48.jpg)
Processes Exercise I
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isobaric =constant pressure process?
(a)
V
p i f
(b)
V
p i
f
(c)
V
p i
f
(d)
V
p i
f
(e) Intentionallyleft blank
For an Isobaric process, Wgas = p (Vf − Vi)
![Page 49: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/49.jpg)
Processes Exercise II
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isothermal =constant temperature process?
![Page 50: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/50.jpg)
Processes Exercise II
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isothermal =constant temperature process?
(a)
V
p i f
![Page 51: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/51.jpg)
Processes Exercise II
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isothermal =constant temperature process?
(a)
V
p i f
(b)
V
p i
f
![Page 52: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/52.jpg)
Processes Exercise II
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isothermal =constant temperature process?
(a)
V
p i f
(b)
V
p i
f
(c)
V
p i
f
![Page 53: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/53.jpg)
Processes Exercise II
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isothermal =constant temperature process?
(a)
V
p i f
(b)
V
p i
f
(c)
V
p i
f
(d)
V
p i
f
![Page 54: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/54.jpg)
Processes Exercise II
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isothermal =constant temperature process?
(a)
V
p i f
(b)
V
p i
f
(c)
V
p i
f
(d)
V
p i
f
(e) Intentionallyleft blank
![Page 55: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/55.jpg)
Processes Exercise II
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isothermal =constant temperature process?
(a)
V
p i f
(b)
V
p i
f
pV = NkBT⇒ pV = constant⇒ hyperbola
(c)
V
p i
f
(d)
V
p i
f
(e) Intentionallyleft blank
![Page 56: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/56.jpg)
Processes Exercise II
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isothermal =constant temperature process?
(a)
V
p i f
(b)
V
p i
f
pV = NkBT⇒ pV = constant⇒ hyperbola
(c)
V
p i
f
(d)
V
p i
f
(e) Intentionallyleft blank
For an Isothermal process, Wgas = NkBT ln
(
Vf
Vi
)
![Page 57: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/57.jpg)
Processes Exercise II
Ideal-Gas Processes 21st July 2014
Which of the following pV diagrams corresponds to an Isothermal =constant temperature process?
(a)
V
p i f
(b)
V
p i
f
pV = NkBT⇒ pV = constant⇒ hyperbola
(c)
V
p i
f
(d)
V
p i
f
(e) Intentionallyleft blank
For an Isothermal process, Wgas = NkBT ln
(
Vf
Vi
)
(c) is an Isochoric process, ⇒ constant volume ⇒ Wgas = 0
![Page 58: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/58.jpg)
First Law for Ideal Gasses
Ideal-Gas Processes 21st July 2014
First Law of Thermodynamics: Q+W = ∆Eth
![Page 59: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/59.jpg)
First Law for Ideal Gasses
Ideal-Gas Processes 21st July 2014
First Law of Thermodynamics: Q+W = ∆Eth
Wgas is the work done by the system ⇒ W = −Wgas
![Page 60: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/60.jpg)
First Law for Ideal Gasses
Ideal-Gas Processes 21st July 2014
First Law of Thermodynamics: Q+W = ∆Eth
Wgas is the work done by the system ⇒ W = −Wgas
For an Ideal Gas: ∆Eth =3
2NkB∆T
![Page 61: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/61.jpg)
First Law for Ideal Gasses
Ideal-Gas Processes 21st July 2014
First Law of Thermodynamics: Q+W = ∆Eth
Wgas is the work done by the system ⇒ W = −Wgas
For an Ideal Gas: ∆Eth =3
2NkB∆T
Q−Wgas =3
2NkB∆T First Law for an Ideal Gas
![Page 62: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/62.jpg)
First Law for Ideal Gasses
Ideal-Gas Processes 21st July 2014
First Law of Thermodynamics: Q+W = ∆Eth
Wgas is the work done by the system ⇒ W = −Wgas
For an Ideal Gas: ∆Eth =3
2NkB∆T
Q−Wgas =3
2NkB∆T First Law for an Ideal Gas
If forced to at gunpoint: Q−Wgas =3
2nR∆T
![Page 63: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/63.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V
p
![Page 64: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/64.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
![Page 65: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/65.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
![Page 66: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/66.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
(a) Q = 5 J
![Page 67: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/67.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
(a) Q = 5 J
(b) Q = 7.5 J
![Page 68: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/68.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
(a) Q = 5 J
(b) Q = 7.5 J
(c) Q = 15 J
![Page 69: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/69.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
(a) Q = 5 J
(b) Q = 7.5 J
(c) Q = 15 J
(d) Q = 17.5 J
![Page 70: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/70.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
(a) Q = 5 J
(b) Q = 7.5 J
(c) Q = 15 J
(d) Q = 17.5 J
(e) Q = 25 J
![Page 71: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/71.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
(a) Q = 5 J
(b) Q = 7.5 J
(c) Q = 15 J
(d) Q = 17.5 J
(e) Q = 25 J
![Page 72: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/72.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
(e) Q = 25 J
Isobaric ⇒ Wgas = p∆V
![Page 73: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/73.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
(e) Q = 25 J
Isobaric ⇒ Wgas = p∆V
Wgas = (5Pa)(
3m3− 1m3
)
= 10J
![Page 74: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/74.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
(e) Q = 25 J
Isobaric ⇒ Wgas = p∆V
Wgas = (5Pa)(
3m3− 1m3
)
= 10J
Constant pressure ⇒ tripling thevolume also triples the temperature
![Page 75: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/75.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
(e) Q = 25 J
Isobaric ⇒ Wgas = p∆V
Wgas = (5Pa)(
3m3− 1m3
)
= 10J
Constant pressure ⇒ tripling thevolume also triples the temperature
⇒ Tf = 7.5K and ∆T = 5 k
![Page 76: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/76.jpg)
First-Law Exercise I
Ideal-Gas Processes 21st July 2014
An ideal gas expands isobarically as shown. If the number ofmolecules in the gas is such that NkB = 2 J/K, how much heatwas involved in this process? Hint: Given the initial pressure andvolume values, the gas’s initial temperature was 2.5K.
V (m3)
p(Pa)
i f
1 3
5
Q−Wgas =3
2NkB∆T ⇒
Q−Wgas =3
2(2)∆T
(e) Q = 25 J
Isobaric ⇒ Wgas = p∆V
Wgas = (5Pa)(
3m3− 1m3
)
= 10J
Constant pressure ⇒ tripling thevolume also triples the temperature
⇒ Tf = 7.5K and ∆T = 5 k
First Law: Q− 10J = 15J
![Page 77: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/77.jpg)
First-Law Exercise II
Ideal-Gas Processes 21st July 2014
The pV diagram shown is for an Adiabatic expansion. (Note: Theshape is NOT a hyperbola.) An adiabatic process is one in whichQ = 0. Which of the following statements about this expansionmust be correct?
V
p i
f
![Page 78: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/78.jpg)
First-Law Exercise II
Ideal-Gas Processes 21st July 2014
The pV diagram shown is for an Adiabatic expansion. (Note: Theshape is NOT a hyperbola.) An adiabatic process is one in whichQ = 0. Which of the following statements about this expansionmust be correct?
V
p i
f
(a) The gas’s temperature musthave decreased during theexpansion.
![Page 79: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/79.jpg)
First-Law Exercise II
Ideal-Gas Processes 21st July 2014
The pV diagram shown is for an Adiabatic expansion. (Note: Theshape is NOT a hyperbola.) An adiabatic process is one in whichQ = 0. Which of the following statements about this expansionmust be correct?
V
p i
f
(a) The gas’s temperature musthave decreased during theexpansion.
(b) The gas’s temperature musthave stayed constant during theexpansion.
![Page 80: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/80.jpg)
First-Law Exercise II
Ideal-Gas Processes 21st July 2014
The pV diagram shown is for an Adiabatic expansion. (Note: Theshape is NOT a hyperbola.) An adiabatic process is one in whichQ = 0. Which of the following statements about this expansionmust be correct?
V
p i
f
(a) The gas’s temperature musthave decreased during theexpansion.
(b) The gas’s temperature musthave stayed constant during theexpansion.
(c) The gas’s temperature musthave increased during theexpansion.
![Page 81: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/81.jpg)
First-Law Exercise II
Ideal-Gas Processes 21st July 2014
The pV diagram shown is for an Adiabatic expansion. (Note: Theshape is NOT a hyperbola.) An adiabatic process is one in whichQ = 0. Which of the following statements about this expansionmust be correct?
V
p i
f
(a) The gas’s temperature musthave decreased during theexpansion.
(b) The gas’s temperature musthave stayed constant during theexpansion.
(c) The gas’s temperature musthave increased during theexpansion.
(d) and (e) Intentionally left blank.
![Page 82: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/82.jpg)
First-Law Exercise II
Ideal-Gas Processes 21st July 2014
The pV diagram shown is for an Adiabatic expansion. (Note: Theshape is NOT a hyperbola.) An adiabatic process is one in whichQ = 0. Which of the following statements about this expansionmust be correct?
V
p i
f
(a) The gas’s temperature musthave decreased during theexpansion.
(b) The gas’s temperature musthave stayed constant during theexpansion.
(c) The gas’s temperature musthave increased during theexpansion.
(d) and (e) Intentionally left blank.
![Page 83: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/83.jpg)
First-Law Exercise II
Ideal-Gas Processes 21st July 2014
The pV diagram shown is for an Adiabatic expansion. (Note: Theshape is NOT a hyperbola.) An adiabatic process is one in whichQ = 0. Which of the following statements about this expansionmust be correct?
V
p i
f
(a) The gas’s temperature musthave decreased during theexpansion.
First Law: Q−Wgas =3
2NkB∆T
![Page 84: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/84.jpg)
First-Law Exercise II
Ideal-Gas Processes 21st July 2014
The pV diagram shown is for an Adiabatic expansion. (Note: Theshape is NOT a hyperbola.) An adiabatic process is one in whichQ = 0. Which of the following statements about this expansionmust be correct?
V
p i
f
(a) The gas’s temperature musthave decreased during theexpansion.
First Law: Q−Wgas =3
2NkB∆T
Adiabatic ⇒ Q = 0 ⇒ −Wgas =3
2NkB∆T
![Page 85: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/85.jpg)
First-Law Exercise II
Ideal-Gas Processes 21st July 2014
The pV diagram shown is for an Adiabatic expansion. (Note: Theshape is NOT a hyperbola.) An adiabatic process is one in whichQ = 0. Which of the following statements about this expansionmust be correct?
V
p i
f
(a) The gas’s temperature musthave decreased during theexpansion.
First Law: Q−Wgas =3
2NkB∆T
Adiabatic ⇒ Q = 0 ⇒ −Wgas =3
2NkB∆T
In an expansion, Vf > Vi ⇒ Wgas is positive ⇒ ∆T is negative
![Page 86: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/86.jpg)
Phase Transitions
Ideal-Gas Processes 21st July 2014
Thermal energy, Eth, is NOT temperature!
![Page 87: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/87.jpg)
Phase Transitions
Ideal-Gas Processes 21st July 2014
Thermal energy, Eth, is NOT temperature!
Thermal energy is the combination of the molecules’ kinetic energyand their potential energy. (Translational Kinetic energy is whatdetermines temperature.)
![Page 88: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/88.jpg)
Phase Transitions
Ideal-Gas Processes 21st July 2014
Thermal energy, Eth, is NOT temperature!
Thermal energy is the combination of the molecules’ kinetic energyand their potential energy. (Translational Kinetic energy is whatdetermines temperature.)
During a phase transition (melting, freezing, evaporating,condensing), the thermal energy of the substance changesbecause of a change in potential energy only. (Energy is releasedwhile making bonds during freezing and condensing. It requiresenergy to break bonds during melting and evaporation.)
![Page 89: Ideal-Gas Processes 21st July 2014 - Physics & Astronomyphysics.unm.edu/Courses/morgan-tracy/151Summer/Slides/151-07-21-… · The Ideal-Gas Equation Ideal-Gas Processes 21st July](https://reader036.fdocuments.in/reader036/viewer/2022081721/5a9e24287f8b9a36788bd85c/html5/thumbnails/89.jpg)
Phase Transitions
Ideal-Gas Processes 21st July 2014
Thermal energy, Eth, is NOT temperature!
Thermal energy is the combination of the molecules’ kinetic energyand their potential energy. (Translational Kinetic energy is whatdetermines temperature.)
During a phase transition (melting, freezing, evaporating,condensing), the thermal energy of the substance changesbecause of a change in potential energy only. (Energy is releasedwhile making bonds during freezing and condensing. It requiresenergy to break bonds during melting and evaporation.)
Since the kinetic energy doesn’t change,There is no change in temperature during a phase transition