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

P_A=nRT_A/V_A=2.49\times10^5\ \mathrm{Pa},\quad P_B=2P_A=4.99\times10^5\ \mathrm{Pa}

problems.proof.analysis

The ideal-gas equation applies at each equilibrium state. Volume is fixed on $AB$ , so doubling the temperature doubles the pressure.