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

\Delta U_{12}=\frac32nR(T_2-T_1)

problems.proof.analysis

Solve the algebraic expression and retain the solution consistent with the physical domain. Checking units helps catch algebraic errors.

problems.proof.pitfall. The stated work sign convention is work done by the gas; use ΔU=Q−W and remember the isochoric leg has zero work.