Practice Final Problems - Universal Physics: Thermal Physics | PHYS 213, Exams of Physics

Download Practice Final Problems - Universal Physics: Thermal Physics | PHYS 213 and more Exams Physics in PDF only on Docsity! Physics 213. Practice Final Problems Spring 2007 Last Name: First Name ID This is a set of practice problems for the final exam. It is not meant to represent every topic and is not meant to be equivalent to a 2-hour exam. These problems have not been carefully tested and there may be errors and inconsistencies. For practice, work the problems closed book. Physics 213. Practice Final Problems Spring 2007 1. Four distinguishable atoms are confined to a box with two sections, as shown. The atoms can move between the sections. Section A has twice the volume of section B. In equilibrium, what is Pb, the probability that all of the atoms will be found in section B? (a) Pb = 1/81 (b) Pb = 1/64 (c) Pb = 1/16 2. An ideal Carnot engine acting as a refrigerator extracts QC joules of heat from the food in the fridge and gives out QH joules of heat to the outside world. The increase of entropy of the outside world is exactly equal to the loss of the entropy by the food. (a) True (b) False 3. Show explicitly the relation of how an ideal Carnot engine leads to the answer you gave for question 2, i.e. show that the increase of entropy of the outside world is [or is not] exactly equal to the loss of the entropy by the food. This will be discussed in the review. 4. Two bricks with the same mass, M = 2 kg, and heat capacity, C = 2100 J/K, but different initial temperatures, T1 = 20° C and T2 = 50° C, are put in thermal contact with each other (but are isolated from the rest of the world). After the two-brick system reaches thermal equilibrium, by how much, ∆Stot, has their total entropy changed? a. ∆Stot = 0.0 J/K b. ∆Stot = 5 J/K c. ∆Stot = 10 J/K d. ∆Stot = 15 J/K e. ∆Stot = 20 J/K 5. The chemical potential is a measure of a. the change of free energy as a particle is added to a system. b. the change of free energy as energy is added to a system. c. the change of potential energy when chemicals are mixed. 6. If you double the absolute temperature of an ideal classical gas (at fixed volume), by what factor do you change the number of times per second that molecules hit the walls? (a) 1 (b) 1.41 (c) 2 (d) 2.82 (e) 4 A B Physics 213. Practice Final Problems Spring 2007 The next 4 questions concern a system of 4 distinguishable spins, each with magnetic moment µ = 9 x 10-23 J/T. 15. How many available microstates are there for this spin system in zero magnetic field? (a) 4 (b) 8 (c) 16 16. What is the entropy of the spins in the macrostate with zero total magnetic moment ? (a) σ = 0 (b) σ = 0.693 (c) σ = 1.386 (d) σ = 1.792 (e) σ = 3.584 17. How many distinct energy levels are there for the 4-spin system in a magnetic field? (a) 4 (b) 5 (c) 16 18. Now the spins are allowed to contact a thermal reservoir at T = 10 K, and the magnetic field is turned up to B = 1 Tesla. Calculate the following ratio of probabilities: R = P(all spins parallel to B) / P(all spins antiparallel to B) (a) R = 7.7 (b) R = 13.6 (c) R = 64 (d) R = 144 (e) R = 184 Physics 213. Practice Final Problems Spring 2007 19. A Carnot heat engine is operated as a refrigerator operating between two reservoirs Tc and Th. One must supply 250 J of work to move 1 kJ of heat from the cold reservoir. If the same engine is operated as a heat engine operating between temperatures Th and Tc what is its efficiency? a. ε = 5% b. ε = 20% c. ε = 33% d. ε = 50% e. ε = 66% 20. If the average square of the velocity vector, i.e. the average square of the speed, of molecules with molecular weight 0.1 kg/mol in an ideal gas is 104 m2/ s2, what is the temperature? (a) 4 K (b) 40 K (c) 400 K (d) 4000 K (e) cannot be determined from this information 21. The latent heat of fusion for a particular liquid-solid transition is 0.35 J/kg. If the freezing temperature is 200 K, what is the entropy change ∆σ per kg when the material melts? (a) 0 (b) 1.75 × 1014 (c) 1.75 × 1016 (d) 1.3 × 1020 (e) 2.6 × 1022 22. There is a 100 W heat leak from a room at temperature 22 °C into an ideal refrigerator. How much electrical power is needed to keep the refrigerator at - 10 °C? (a) 12 W (b) 22 W (c) 45 W (d) 64 W (e) 164 W Physics 213. Practice Final Problems Spring 2007 23. A particular molecule has three states, with energy spacing ε = 10-20 J, as shown. At 1000K, what is P0, the probability that the molecule is in the ground state? (a) P0 = 0.33 (b) P0 = 0.46 (c) P0 = 0.58 (d) P0 = 0.67 (e) P0 = 1.00 24. At what altitude is the atmospheric pressure of oxygen (molar mass = 32 g/mol) only 10% of that on the surface of the earth? (Assume T = 250K everywhere) (a) 15.3 km (b) 17.5 km (c) 21.3 km (d) 25.1 km (e) 27.3 km 25. A sample of N2 gas, initially with volume Vi = 0.5 m3 and temperature Ti = 300 K, expands adiabatically to Vf = 1.2 m3, pushing on a piston. What is Tf, the final temperature of the N2? Assume that nitrogen is an ideal diatomic gas. (a) Tf = 125 K (b) Tf = 211 K (c) Tf = 258 K (d) Tf = 367 K (e) Tf = 426 K 26. Six moles of an ideal monatomic gas is heated at constant volume from 3000K to 600oK. What is ∆S, the change in the entropy of the gas? (a) ∆S = 51.8 J/K (b) ∆S = 98.7 J/K (c) ∆S = 149.6 J/K (d) ∆S = 212.4 J/K (e) ∆S = 1065 J/K } }ε ε E