The Physics
Hypertextbook
Opus in profectus

# Pressure-Volume Diagrams

## Practice

### practice problem 1

One mole of an ideal, monatomic gas runs through a four step cycle. All processes are either isobaric or isochoric. The pressure and volume of the gas at the extreme points in the cycle are given in the first two data rows of the table below.
1. Sketch the PV graph of this cycle.
2. Determine the temperature at state A, B, C, and D.
3. Calculate W, Q, and ΔU on the path A→B, B→C, C→D, D→A and for one complete cycle. (Include the algebraic sign with each value.)
4. Does this cycle behave more like an engine or a refrigerator?
state A B C D
P (Pa) 100,000 200,000 200,000 100,000
V (m3) 0.020 0.020 0.060 0.060
T (K)
path A→B B→C C→D D→A ABCDA
description isochoric isobaric isochoric isobaric closed cycle
ΔU (J)
Q (J)
W (J)
A Four Step Cycle (Isobaric & Isochoric)

#### solution

state A B C D
P (Pa) 100,000 200,000 200,000 100,000
V (m3) 0.020 0.020 0.060 0.060
T (K) 240 480 1,440 720
path A→B B→C C→D D→A ABCDA
description isochoric isobaric isochoric isobaric closed cycle
ΔU (J) +3,000 +12,000 −9,000 −6,000 0
Q (J) +3,000 +20,000 −9,000 −10,000 +4,000
W (J) 0 −8,000 0 +4,000 −4,000
A Four Step Cycle (Isobaric & Isochoric)

### practice problem 2

Write something else.

### practice problem 3

Write something different.