Thermodynamics and Statistical Mechanics First Law of Thermodynamics.
Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of...
Transcript of Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of...
![Page 1: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/1.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Chapter 3 - First Law of Thermodynamics
The ideal gas law is a combination of three intuitiverelationships between pressure, volume, temp and moles.
David J. StarlingPenn State Hazleton
Fall 2013
![Page 2: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/2.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
First Law of Thermo
When a gas expands, it does work on its
surroundings equal to
W =
∫~F · d~s =
∫(pA)(ds) =
∫p(A ds)
W =
∫ Vf
Vi
p dV
![Page 3: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/3.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
First Law of Thermo
We can graph p vs. volume—the area under the
curve is work done.
Use an inflated balloon to visualize the process.
![Page 4: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/4.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
First Law of Thermo
We can graph p vs. volume—the area under the
curve is work done.
Use an inflated balloon to visualize the process.
![Page 5: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/5.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
First Law of Thermo
The thermodynamic quantities heat and work
alter the energy of a system according to the first
law of thermodynamics:
∆Eint = Q − W (1)
dEint = dQ − dW (2)
Heat increases the internal energy of the system, but workdecreases the internal energy of the system.
![Page 6: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/6.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
First Law of Thermo
The thermodynamic quantities heat and work
alter the energy of a system according to the first
law of thermodynamics:
∆Eint = Q − W (1)
dEint = dQ − dW (2)
Heat increases the internal energy of the system, but workdecreases the internal energy of the system.
![Page 7: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/7.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
First Law of Thermo
There are four very important cases involving the
first law of thermodynamics.
![Page 8: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/8.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
First Law of Thermo
Which one of the following statements is not consistent withthe first law of thermodynamics?
(a) The internal energy of a finite system must be finite.
(b) An engine may be constructed such that the work doneby the machine exceeds the energy input to the engine.
(c) An isolated system that is thermally insulated cannotdo work on its surroundings nor can work be done onthe system.
(d) The internal energy of a system decreases when it doeswork on its surroundings and there is no flow of heat.
(e) An engine may be constructed that gains energy whileheat is transferred to it and work is done on it.
![Page 9: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/9.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
When heat is added to a gas at constant volume,
its temperature changes according to
Q = nCV∆T (3)
I CV is the molar specific heat at constant volumeI From first law ∆Eint = Q − W = Q = nCV∆T ,
CV =∆Eint
n∆T=
32 nRTn∆T
=32
R (4)
![Page 10: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/10.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
When heat is added to a gas at constant volume,
its temperature changes according to
Q = nCV∆T (3)
I CV is the molar specific heat at constant volumeI From first law ∆Eint = Q − W = Q = nCV∆T ,
CV =∆Eint
n∆T=
32 nRTn∆T
=32
R (4)
![Page 11: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/11.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
When heat is added to a gas at constant volume,
its temperature changes according to
Q = nCV∆T (3)
I CV is the molar specific heat at constant volumeI From first law ∆Eint = Q − W = Q = nCV∆T ,
CV =∆Eint
n∆T=
32 nRTn∆T
=32
R (4)
![Page 12: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/12.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
When heat is added to a gas at constant pressure,
its temperature again changes according to
Q = nCp∆T (5)
I W = p∆V = nR∆T
∆Eint = nCV∆T = Q − W
nCV∆T = nCp∆T − nR∆T
CV = Cp − R
Cp = CV + R
![Page 13: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/13.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
When heat is added to a gas at constant pressure,
its temperature again changes according to
Q = nCp∆T (5)
I W = p∆V = nR∆T
∆Eint = nCV∆T = Q − W
nCV∆T = nCp∆T − nR∆T
CV = Cp − R
Cp = CV + R
![Page 14: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/14.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
When heat is added to a gas at constant pressure,
its temperature again changes according to
Q = nCp∆T (5)
I W = p∆V = nR∆T
∆Eint = nCV∆T = Q − W
nCV∆T = nCp∆T − nR∆T
CV = Cp − R
Cp = CV + R
![Page 15: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/15.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
When heat is added to a gas at constant pressure,
its temperature again changes according to
Q = nCp∆T (5)
I W = p∆V = nR∆T
∆Eint = nCV∆T = Q − W
nCV∆T = nCp∆T − nR∆T
CV = Cp − R
Cp = CV + R
![Page 16: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/16.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
When heat is added to a gas at constant pressure,
its temperature again changes according to
Q = nCp∆T (5)
I W = p∆V = nR∆T
∆Eint = nCV∆T = Q − W
nCV∆T = nCp∆T − nR∆T
CV = Cp − R
Cp = CV + R
![Page 17: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/17.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
When heat is added to a gas at constant pressure,
its temperature again changes according to
Q = nCp∆T (5)
I W = p∆V = nR∆T
∆Eint = nCV∆T = Q − W
nCV∆T = nCp∆T − nR∆T
CV = Cp − R
Cp = CV + R
![Page 18: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/18.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
Molecules can store energy based upon their
geometries, altering their specific heats.
Each degree of freedom gets about
I 12 kT energy per molecule
I 12 RT energy per mole
![Page 19: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/19.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
Molecules can store energy based upon their
geometries, altering their specific heats.
Each degree of freedom gets about
I 12 kT energy per molecule
I 12 RT energy per mole
![Page 20: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/20.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
Molecules can also store vibrational energy, but
only at higher temperatures.
![Page 21: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/21.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Molar Specific Heat
A monatomic gas particle has only 3 degrees of freedomand each particle in the gas has a thermal energy equal to(3/2)kT . How many degrees of freedom does a diatomicgas particle have and how much thermal energy does eachmolecule have?
(a) 2, kT
(b) 3, (3/2)kT
(c) 4, 2kT
(d) 5, (5/2)kT
(e) 6, 3kT
![Page 22: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/22.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
Adiabatic expansion means that the volume
changes while Q = 0; i.e., no heat is transferred.
Let’s derive the curve in (b) from first principles!
![Page 23: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/23.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
There is no heat transfer, Q = 0, so the first law reads:
dEint = −p dV
nCV dT = −p dV
n dT =−p dV
CV
Taking partials of the ideal gas law and using Cp = CV + R,
p dV + V dp = nR dT
n dT =p dV + V dp
R
=p dV + V dp
Cp − CV
−p dVCV
=p dV + V dp
Cp − CV
0 =dpp
+Cp
CV
dVV
![Page 24: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/24.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
There is no heat transfer, Q = 0, so the first law reads:
dEint = −p dV
nCV dT = −p dV
n dT =−p dV
CV
Taking partials of the ideal gas law and using Cp = CV + R,
p dV + V dp = nR dT
n dT =p dV + V dp
R
=p dV + V dp
Cp − CV
−p dVCV
=p dV + V dp
Cp − CV
0 =dpp
+Cp
CV
dVV
![Page 25: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/25.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
There is no heat transfer, Q = 0, so the first law reads:
dEint = −p dV
nCV dT = −p dV
n dT =−p dV
CV
Taking partials of the ideal gas law and using Cp = CV + R,
p dV + V dp = nR dT
n dT =p dV + V dp
R
=p dV + V dp
Cp − CV
−p dVCV
=p dV + V dp
Cp − CV
0 =dpp
+Cp
CV
dVV
![Page 26: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/26.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
There is no heat transfer, Q = 0, so the first law reads:
dEint = −p dV
nCV dT = −p dV
n dT =−p dV
CV
Taking partials of the ideal gas law and using Cp = CV + R,
p dV + V dp = nR dT
n dT =p dV + V dp
R
=p dV + V dp
Cp − CV
−p dVCV
=p dV + V dp
Cp − CV
0 =dpp
+Cp
CV
dVV
![Page 27: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/27.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
There is no heat transfer, Q = 0, so the first law reads:
dEint = −p dV
nCV dT = −p dV
n dT =−p dV
CV
Taking partials of the ideal gas law and using Cp = CV + R,
p dV + V dp = nR dT
n dT =p dV + V dp
R
=p dV + V dp
Cp − CV
−p dVCV
=p dV + V dp
Cp − CV
0 =dpp
+Cp
CV
dVV
![Page 28: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/28.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
There is no heat transfer, Q = 0, so the first law reads:
dEint = −p dV
nCV dT = −p dV
n dT =−p dV
CV
Taking partials of the ideal gas law and using Cp = CV + R,
p dV + V dp = nR dT
n dT =p dV + V dp
R
=p dV + V dp
Cp − CV
−p dVCV
=p dV + V dp
Cp − CV
0 =dpp
+Cp
CV
dVV
![Page 29: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/29.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
There is no heat transfer, Q = 0, so the first law reads:
dEint = −p dV
nCV dT = −p dV
n dT =−p dV
CV
Taking partials of the ideal gas law and using Cp = CV + R,
p dV + V dp = nR dT
n dT =p dV + V dp
R
=p dV + V dp
Cp − CV
−p dVCV
=p dV + V dp
Cp − CV
0 =dpp
+Cp
CV
dVV
![Page 30: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/30.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
There is no heat transfer, Q = 0, so the first law reads:
dEint = −p dV
nCV dT = −p dV
n dT =−p dV
CV
Taking partials of the ideal gas law and using Cp = CV + R,
p dV + V dp = nR dT
n dT =p dV + V dp
R
=p dV + V dp
Cp − CV
−p dVCV
=p dV + V dp
Cp − CV
0 =dpp
+Cp
CV
dVV
![Page 31: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/31.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
Integrating this equation, we find
ln p +Cp
CVln V = constant
ln(
pVCp/CV)
= constant
pVCp/CV = pVγ = constant
This results describes the adiabat in the p − V plane.
This also implies (using ideal gas law):
piVγi = pf V
γf
TiVγ−1i = Tf V
γ−1f
![Page 32: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/32.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
Integrating this equation, we find
ln p +Cp
CVln V = constant
ln(
pVCp/CV)
= constant
pVCp/CV = pVγ = constant
This results describes the adiabat in the p − V plane.
This also implies (using ideal gas law):
piVγi = pf V
γf
TiVγ−1i = Tf V
γ−1f
![Page 33: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/33.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
Integrating this equation, we find
ln p +Cp
CVln V = constant
ln(
pVCp/CV)
= constant
pVCp/CV = pVγ = constant
This results describes the adiabat in the p − V plane.
This also implies (using ideal gas law):
piVγi = pf V
γf
TiVγ−1i = Tf V
γ−1f
![Page 34: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/34.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
Integrating this equation, we find
ln p +Cp
CVln V = constant
ln(
pVCp/CV)
= constant
pVCp/CV = pVγ = constant
This results describes the adiabat in the p − V plane.
This also implies (using ideal gas law):
piVγi = pf V
γf
TiVγ−1i = Tf V
γ−1f
![Page 35: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/35.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
Integrating this equation, we find
ln p +Cp
CVln V = constant
ln(
pVCp/CV)
= constant
pVCp/CV = pVγ = constant
This results describes the adiabat in the p − V plane.
This also implies (using ideal gas law):
piVγi = pf V
γf
TiVγ−1i = Tf V
γ−1f
![Page 36: Chapter 3 (Volume 2) - First Law of Thermodynamics · Chapter 3 (Volume 2) - First Law of Thermodynamics First Law of Thermo Molar Specific Heat Adiabatic Expansion First Law of](https://reader031.fdocuments.in/reader031/viewer/2022021522/5b89ad477f8b9abe1e8e2891/html5/thumbnails/36.jpg)
Chapter 3 (Volume 2) -First Law of
Thermodynamics
First Law of Thermo
Molar Specific Heat
Adiabatic Expansion
Adiabatic Expansion
Consider the following pressure-volume graphs. Which ofthese graphs represents the behavior of a gas undergoingfree expansion?
E. None of the graphs represent a gas undergoing freeexpansion.