Problem 2
One mole of monatomic ideal gas initially at temperature expands isobarically until its volume doubles, then cools isochorically to . Find the maximum temperature, work and heat in each stage, and total work. Use . 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
At constant pressure the ideal-gas law makes proportional to ; doubling volume gives . 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.