Problem 2

One mole of monatomic ideal gas starts at state

A

with

T_A=300

K and

V_A=0.010

^3

. It follows a three-step cycle: (1) heat at constant volume from

A

B

, where

T_B=600

K; (2) expand isothermally from

B

C

until the volume doubles; (3) compress at constant pressure from

C

back to

A

. Use

R=8.31

J mol

^{-1}

^{-1}

, molar

C_V=3R/2

, and define work

W

as positive when done by the gas. (a) Find the pressures at

A,B,C

. (b) Calculate work and heat for each leg. (c) Check the first law over the complete cycle.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

W_{BC}=nRT_B\ln(V_C/V_B)=600R\ln2=3453\ \mathrm J,\quad \Delta U_{BC}=0,\quad Q_{BC}=W_{BC}

problems.proof.analysis

For an ideal gas, constant temperature means no change in internal energy. Integrating $P=nRT/V$ over volume gives the logarithmic work, and the first law then requires $Q=W$ .

problems.proof.pitfall. Expansion work is positive; do not set

Q=0

merely because temperature is constant—the gas must absorb heat to supply the work.