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

\boxed{V_1=\frac{nRT_1}{p_1}=0.02493\,\mathrm{m^3},\ V_{max}=V_2=0.04986\,\mathrm{m^3};\ W_{12}=2.493\,\mathrm{kJ},\ \Delta U_{12}=3.740\,\mathrm{kJ},\ Q_{12}=6.233\,\mathrm{kJ};\ p_3=5.00\times10^4\,\mathrm{Pa},\ W_{cycle}=2.493\,\mathrm{kJ}}

problems.proof.analysis

Collect answers to every part, including signs, directions, and image or process properties where relevant. Dimensions match the physical quantities.