Thermodynamics unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Maxwell-Boltzmann distribution
Why a PV cycle's enclosed area is net work
Entropy and probability
Kelvin is not optional
Specific heat and phase change
Ideal gas process on a PV diagram
Root-mean-square speed
Ideal gas law
Coefficient of performance
Heat vs temperature vs internal energy
Temperature is not heat
Isochoric
Short answer 1. Define or explain: Conduction, convection, radiation
3 ptsShort answer 2. Define or explain: Efficiency and the Carnot ceiling
3 ptsShort answer 3. Define or explain: Why work is path-dependent
3 ptsShort answer 4. Define or explain: First law of thermodynamics
3 ptsFree response
10 ptsMATHEMATICAL ROUTINES (Question 1, 10 points). A sample of n moles of a monatomic ideal gas is in a large, sealed, thermally conducting container of fixed volume. A small sphere of mass mS (volume negligible next to the container's) is inside, initially in thermal equilibrium with the gas. The gas is initially in State X with pressure P and volume V. The gas is heated until it reaches State Y with pressure 3P, and the sphere is again in thermal equilibrium with the gas. The total energy transferred to the sphere during the heating is QS. (Figure 2 shows the Maxwell-Boltzmann speed distribution for State X — number of atoms per unit speed versus atom speed.) For B: an insulated container holds a liquid of mass mL and specific heat cL. The original sphere (mass mS < mL, specific heat cS < cL) is submerged in the liquid, starting hotter than the liquid; they reach thermal equilibrium, with temperature-change magnitudes |ΔTL| and |ΔTS|.
A(i). Describe the curve on Figure 3 that could represent the atoms-per-unit-speed distribution for State Y, compared with the State X curve.
A(ii). Derive an expression for the change ΔT in gas temperature from State X to State Y, in terms of n, P, V, and physical constants, as appropriate.
A(iii). Derive an expression for the specific heat cS of the sphere, in terms of n, mS, P, V, QS, and physical constants, as appropriate.
B. Indicate whether |ΔTS| is greater than, less than, or equal to |ΔTL|, and justify with conceptual reasoning beyond algebraic solutions.