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

\sum\Delta U=0,\quad \sum W=960\ \mathrm J,\quad \sum Q=960\ \mathrm J;\qquad Q_{AB}=3739.5\ \mathrm J,\ Q_{BC}=3453\ \mathrm J,\ Q_{CA}=-6232.5\ \mathrm J

problems.proof.analysis

After a full cycle the gas returns to its initial state, so its net internal-energy change is zero. The net work is $-2493+3453=960$ J and net heat is $3739.5+3453-6232.5=960$ J, consistent with $\Delta U=Q-W=0$ .