# Laws of Thermodynamics Chapter 18

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27 Οκτ 2013 (πριν από 4 χρόνια και 6 μήνες)

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Laws of Thermodynamics

Chapter 18

I.

Outcomes

-

Be able to
:

a.

Distinguish between the change in internal energy of a system, the work done by the
system, and the heat added into the system
.

b.

Be able to understand the sign convention of the First Law of Thermodynamics.

c.

Distinguish between the
different thermal processes.

d.

Understand the natural flow of heat.

e.

Calculate the efficiency of an engine.

f.

Understand how heat pumps work.

II.

Formulas

Work on/by a thermodynamic system
:
W =
-
P∆V

First Law of Thermodynamics
:

U = Q + W

Efficiency of an engi
ne:

|

|

Carnot efficiency
:

Type of Process or Step

Definition

Result in First Law

Isothermal process

T = 0 → ∆U = 0

Q =
-
W

ATiaba瑩c proceVV

Q = 0

U = W

IVocUoric or IVovolu浥瑲ic
proceVV

V = 0 → W = 0

U = Q

III.

s,

homework problems
, and labs

a.

First Law of Thermodynamics

(1
8
-
1
&

1
8
-
2
)

610

613.

Do P.
643

-

644

(
3
,
5,
11
)
.

b.

Thermal Processes (18
-

621. Do P. 644

645 (13, 15, 17, 23, 27).

c.

Heat Engines and Carnot Cycle (18
-
625

629. Do P. 646 (49, 51).

d.

Heat Pumps and Entropy (18
-
7 & 18
-

640. Do P. 646

647 (55, 59,
63
-
65).

e.

Review extra credit: P. 647

648 (74, 80, 84, 93)

IV.

Recommendations for further understanding

The material in Section 18
-
4 on mola
r specific heats is not on the AP Exam; however, the
constant volume, constant pressure, and adiabatic concepts are important.

Review Section 18
-
6 on heat engines and Carnot cycle.

Chapter 18: Laws of Thermodynamics

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Entropy (Section 18
-
8) is an important concept, but calculations are not
included.

Chapter Summary on pages 640

642.

Look online at Mrs. Stob’s St. Croix webpage to find videos and other helpful links to help
understand the material and to study for the test.

V.

Reminders

The most recent equation written for the First Law of
Thermodynamics

on the AP
equation sheet is:

U = Q + W
.

This means that work done on a system is positive. It is
important to remember positives and negatives when talking about work. You will find
an extra study guide concerning the conventions of the

signs on work in other topics in
physics.

All temperatures should be converted to Kelvins in ideal gas equations.

Work done
on

a system is positive (decrease in gas volume) and work done
by

a system is
negative (increase in gas volume).

On a P
-
V diagram,
the work done for any step in a process is the area between the P
-
V
curve and the
x
-
axis. The work done for any process described by a set of steps in a
closed loop is the area enclosed by the loop.

For a complete cycle on a P
-
V diagram (where the cycle r
eturns to original state
conditions of pressure and volume), the temperature also returns to original
temperature. Therefore, the ∆T is zero and the change in internal energy for the cycle is
also zero.

Chapter 18: Laws of Thermodynamics

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P a g e

VI
.

AP Problem

due on the day of the unit test.

The diagram above of pressure
P

versus volume
V

shows the expansion of 2.0 moles of a monatomic
ideal gas from state
A

to state
B
. As shown in the diagram,
P
A

= P
B

= 600 N/m
2
,
V
A

= 3.0 m
3
, and
V
B

= 9.0
m
3
.

(a)

i.

Calculat
e the work done
by the gas

as it expands.

ii.

Calculate the change in internal energy of the gas as it expands.

iii.

Calculate the heat added to or removed from the gas during this expansion.

(b)

The pressure is then reduced to 200 N/m
2

without changing the volume as the gas is taken from
state
B

to state
C
. Label state
C

on the diagram and draw a line or curve to represent the process
from state
B

to state
C
.

(c)

The gas is then compressed isothermally back to state
A
.

i.

Draw a line or
curve on the diagram to represent this process.

ii.

Is heat added to or removed from the gas during this isothermal compression?

_____ removed from

Chapter 18: Laws of Thermodynamics

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Extra notes on Work

Mechanical work done against a gravitational force:

Work done against gravity, e.g., in lifting an object, is positive work.

Work done with gravity, e.g., in lowering an object, is negative work.

Positive work done on a system increases the potential energy of that system.

W = F∆x cos

, where maximum work
is done when the external force doing the work and
the displacement are in the same direction.

Mechanical work done against a spring force:

Work done in stretching or compressing a spring, i.e., work done against the spring force, is
positive.

Positive
work done on a spring
-
mass system increases the potential energy of that system.

Mechanical work done against an electrical force:

Work done in moving a positively charged particle toward another positively charged
particle, i.e., against
the electric fields lines and against the electric force on that particle, is
positive work. Likewise, work done in moving a negatively charged particle toward another
negatively charged particle is positive work.

Positvie work done in each case increases

the potential energy of the system.

W = ∆U = q∆V

[If q is positive, positive work is done when ∆V is positive; i.e., the particle is
moved from lower potential to higher potential, as is the case when moving toward another
positive charge. If q is negat
ive, positive work is done when ∆V is negative; i.e., the particle is
moved from higher potential to lower potential, as is the case when moving toward a
negative particle.]

Work done on a thermodynamic system:

Work done in compressing a system of ideal ga
s particles is positive, since it increases the
potential energy of the system of particles.

Since
W =
-
P∆V
, at constant pressure, if volume decreases,

V

is negative and work done is
positive.

U = Q + W
, where +W is work done on the system, so it produce
s a positive ∆U, and +Q is
heat added to the system, so it also produces a positive ∆U.