Problem 2

One mole of monatomic ideal gas at

T_1=300,\,\mathrm{K}

p_1=1.0\times10^5,\,\mathrm{Pa}

is heated at constant pressure to

T_2=600,\,\mathrm{K}

, then cooled at constant volume back to

T_1

to complete a cycle. Use

R=8.31,\,\mathrm{J,mol^{-1}K^{-1}}

and take

W>0

as work done by the gas. (a) Find initial and maximum volume. (b) For the isobaric leg, find

W,\Delta U,Q

. (c) Find final pressure and net cycle work. Keep the sign convention consistent and use appropriate SI units throughout. Each part builds on intermediate results from the preceding part; apply a physical relation only where the stated model assumptions hold. Finally compare the answers with the initial conditions, expected trends, and an independent check when available.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

W_{12}=p_1(V_2-V_1)=nR(T_2-T_1)

problems.proof.analysis

Combine equations to eliminate intermediate quantities and isolate the desired result. This uses the system’s constraint or conservation law.