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

\boxed{W_2=0,\quad Q_2=\Delta U_2=-9RT_0/4,\quad W_{tot}=RT_0}

problems.proof.analysis

Apply the model consistently to each part, then check dimensions and physical limits.