Thermodynamics systems

Thermodynamics systems

• A thermodynamic system is any collection of objects that

may exchange energy with its surroundings.

• The popcorn in the pot is a thermodynamic system.

• In the thermodynamic process shown here, heat is added to

the system, and the system does

work on its surroundings to lift

the lid of the pot.

© 2016 Pearson Education Inc.

Thermodynamics systems

• In a thermodynamic process,

changes occur in the state of

the system.

• Careful of signs!

• Q is positive when heat flows

into a system.

• W is the work done by the

system, so it is positive for

expansion.


© 2017 Pearson Education, Inc. Slide 18-3

Ideal-Gas Processes

An ideal-gas process can be represented on a graph of pressure versus volume, called a pV diagram.

Knowing p and V, and assuming that n is known for a sealed container, we can find the temperature Tby using the ideal-gas law.

Here is a pV diagram showing three states of a system consisting of 1 mol

of gas.

There are infinitely many

ways to change the gas

from state 1 to state 3.


Ideal-Gas Processes

(a) If you slowly pull a piston

out, you can reverse the

process by slowly pushing

the piston in.

This is called a quasi-static

process.

(b) is a sudden process,

which cannot be represented

on a pV diagram.

Quasi-static processes keep

the system in thermal

equilibrium.

Work done during volume changes

• We can understand the work done by a gas in a volume

change by considering a molecule in the gas.

• When one such molecule collides with a surface moving to

the right, so the volume of the gas increases, the molecule

does positive work on the piston.



• If the piston moves toward the left as in the figure shown

here, so the volume of the gas decreases; positive work is

done on the molecule during the collision.

• Hence the gas molecules do negative work on the piston.



• The infinitesimal work

done by the system during

the small expansion dx is

dW = pA dx.

• In a finite change of

volume from V1 to V2:


Work on a pV-diagram

• The work done equals the area under the curve on a

pV-diagram.

• Shown in the graph is a system

undergoing an expansion with

varying pressure.



• Shown in the graph is a system undergoing a compression

with varying pressure.

• In this case the work is

negative.



• Shown in the graph is a system undergoing an expansion with

constant pressure.

• In this case, W = p(V2 – V1)


Example 1 – As an ideal gas undergoes an isothermal

(constant-temperature) expansion at temperature T, its

volume changes from V1 to V2. How much work does the

gas do?

Work depends on the path chosen: Slide 1 of 4

• Consider three different paths on a pV-diagram for getting

from state 1 to state 2.



• The system does a large amount of work under the path



• The system does a small amount of work under the path



• Along the smooth curve from 1 to 2, the work done is

different from that for either of the other paths.


This p-V diagram shows two

ways to take a system from state

a (at lower left) to state c (at

upper right):

• via state b (at upper left), or

• via state d (at lower right)

For which path is W > 0?

A. path abc only

B. path adc only

C. both path abc and path adc

D. neither path abc nor path adc

QuickCheck

First law of thermodynamics

• The change in the internal energy U of a system is equal to

the heat added minus the work done by the system:

• The first law of thermodynamics is just a generalization of

the conservation of energy.

• Both Q and W depend on the path chosen between states, but

is independent of the path.

• If the changes are infinitesimal, we write the first law as

dU = dQ – dW.



• In a thermodynamic process, the internal energy U of a

system may increase.

• In the system shown below, more heat is added to the system

than the system does work.

• So the internal energy of the system increases.




system may decrease.

• In the system shown below, more heat flows out of the

system than work is done.

• So the internal energy of the system decreases.




system may remain the same.

• In the system shown below, the heat added to the system

equals the work done by the system.

• So the internal energy of the system is unchanged.


© 2016 Pearson Education, Inc.

You put a flame under a piece of metal, raising the temperature of

the metal and making the metal expand. The metal is surrounded

by air. What are the signs of ∆U, Q, and W for the metal in this

process?

A. ∆U > 0, Q > 0, W > 0

B. ∆U < 0, Q > 0, W > 0

C. ∆U > 0, Q > 0, W < 0

D. ∆U < 0, Q > 0, W < 0

QuickCheck


An isothermal process is one for which the temperature of a specific amount of gas is held constant (no change in total thermal energy).

An isochoric process is one for which the volume of the gas is held constant.

An adiabatic process is one in which no heat energy is transferred.

The First Law of Thermodynamics

∆𝐸𝑡ℎ= 𝑄 −𝑊


A cylinder of gas has a frictionless but tightly

sealed piston of mass M. Small masses are

placed onto the top of the piston, causing it to

slowly move downward. A water bath keeps

the temperature constant. In this process:

A. Q > 0

B. Q = 0

C. Q < 0

D. There’s not enough information to say anything about the

heat.

QuickCheck


A system can be taken from state a

to state b along any of the three

paths shown in the p-V diagram. If

state b has greater internal energy

than state a, along which path is the

absolute value |Q| of the heat

transfer the greatest?

A. path 1

B. path 2

C. path 3

D. |Q| is the same for all three paths.

QuickCheck


A system can be taken from state a

to state b along any of the three

paths shown in the p-V diagram. If

state b has greater internal energy

than state a, along which path is

there a net flow of heat out of the

system?

A. path 1

B. path 3

C. all of paths 1, 2, and 3

D. none of paths 1, 2, or 3

QuickCheck

Example 2 – You propose to climb several flights of stairs

to work off the energy you took in by eating a 900-calorie

hot fudge sundae. How high must you climb? Assume

your mass is 80.0 kg and a 25% efficiency of converting

food energy to mechanical energy.

Example 3 – One gram of water (1 cm3) becomes 1671

cm3 of steam when boiled at a constant pressure of 1 atm.

Compute the work done by the water when it vaporizes

and its increase in internal energy

Note: The increase in internal energy is used to dissociate the water molecules as

it turns to steam. It will not increase the temperature of the steam.

Example 4 – The figure below shows a pV-diagram for a cyclic

process in which the initial and final states of some thermodynamic

system are the same. The state of the system starts at point a and

proceeds counterclockwise in the diagram to point b, then back to a;

the total work is W = -500J. Why is the work negative? Also, Find the

change in internal energy and the heat added during this process.

In-class Activity #1 – The pV-diagram below shows a series of

thermodynamic processes. In process ab, 150 J of heat is added to

the system; in process bd, 600 J heat is added. Find

(a) the internal energy change in process ab;

(b) the internal energy change in process abd; and

(c) the total heat added in process acd.


There are three ideal-gas processes in which one of the three terms in the

first law—∆Eth, W, or Q—is zero:

• Isothermal process (∆ Eth = 0): If the temperature of a gas doesn’t

change, neither does its thermal energy. So, the first law is W = Q.

• Isochoric process (W = 0): Work is done on (or by) a gas when its

volume changes. An isochoric process has ∆V = 0; thus no work is done

and the first law can be written ∆Eth = Q.

• Adiabatic process (Q = 0): A process in which no heat is transferred—

perhaps the system is extremely well insulated—is called an adiabatic

process. The system is thermally isolated from its environment.

With Q = 0,the first law is ∆Eth = – W.

Isobaric process: The pressure remains constant, so W = p(V2 – V1).

Special Ideal-Gas Processes

The four processes on a pV-diagram

• Shown are the paths on a pV-diagram for all four different

processes for a constant amount of an ideal gas, all starting at

state a.



What type of gas process is this?

A. Isochoric

B. Isobaric

C. Isothermal

D. Adiabatic

E. None of the above

QuickCheck


An ideal gas is taken around the

cycle shown in this p-V diagram,

from a to b to c and back to a.

Process b c is isothermal. For

process a b,

A. Q > 0, ∆U > 0

B. Q > 0, ∆U = 0

C. Q = 0, ∆U > 0

D. Q = 0, ∆U < 0

QuickCheck






process b c,

A. Q > 0, ∆U > 0

B. Q > 0, ∆U = 0

C. Q = 0, ∆U > 0

D. Q = 0, ∆U < 0

QuickCheck






process c a,

A. Q > 0, ∆U > 0

B. Q = 0, ∆U > 0

C. Q = 0, ∆U < 0

D. Q < 0, ∆U < 0

QuickCheck






this complete cycle,

A. Q > 0, W > 0, U = 0

B. Q < 0, W > 0, U = 0

C. Q = 0, W > 0, U < 0

D. Q = 0, W < 0, U > 0

QuickCheck

Thermodynamics systems

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