Problem 2

One mole of monatomic ideal gas initially at temperature

T_0

expands isobarically until its volume doubles, then cools isochorically to

T_0/2

. Find the maximum temperature, work and heat in each stage, and total work. Use

C_V=3R/2

. 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.prevStep problems.proof.nextStep

W_1=RT_0,\quad \Delta U_1=3RT_0/2,\quad Q_1=5RT_0/2

problems.proof.analysis

Isobaric work $P \Delta V$ is $RT_0$ ; monatomic internal energy rises by $3R \Delta T/2$ . The first law gives absorbed heat $Q_1=W_1+\Delta U_1$ . 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.