Problem 2
One mole of monatomic ideal gas at temperature T0 expands reversibly and isothermally from V0 to 2V0, then is cooled isochorically to T0/2. Find work and heat in each stage, and the gas's total entropy change. Use gas constant R. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.
problems.proof.stepOf
problems.proof.analysis
Work done is the integral of p dV = RT0 ln 2. An ideal gas has no internal-energy change isothermally, so absorbed heat equals work. This follows from the chosen physical model and the stated initial conditions; the sign convention must remain consistent throughout. A dimensional check catches algebraic errors before the result is interpreted.
problems.proof.pitfall. Do not mix sign conventions or omit a system constraint; check the sign and units before interpreting the result.