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rev session 1 - 1 a Define the coefficient of performance...

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Unformatted text preview: 1. a) Define the coefficient of performance for a refrigerator in terms of Q_in, Q_out, and W_net (hint: "what you want"/"what you have to put in") b) Consider the cycle shown (see solutions). How do you know it can be used for refrigeration? Explain how this works, qualitatively. c) Find the coefficient of performance of the cycle in terms of the labeled variables, given that the refrigerator uses an ideal gas, the curve is an adiabat, the gas's adiabatic index is gamma, and the gas has d degrees of freedom. 2. A refrigerator has inner dimensions x, y, and z, and has walls of thickness w (w << x, y, z) with coefficient of thermal conductivity k. It contains an ideal gas which it maintains at temperature T_L, whereas outside the air temperature is T_H. a) If its coefficient of performance is K, find how much power it must draw in order to maintain this temperature difference b) Find the rate at which the entropy of the gas in the refrigerator plus the air outside changes. Is your result consistent with the second law of thermodynamics? If not, why not? 3. You have n moles of oxygen in a rigid, insulated container, and n moles of helium in a separate, identical container. Each gas has exactly the same total internal energy, E. If you bring the two into thermal contact, will heat flow from one to the other? If not, why not? If so, which way, and by how much will the total entropy of the two gases change in reaching thermal equilibrium? 4. A large, heavy metal box of mass m is half filled with a mass M of water at temperature T_0. It is connected by a chain to a truck for no good reason, and at t=0 the truck begins driving at speed v down a long road, dragging the box behind it. If the coefficient of kinetic friction between the box and the road is mu, how long will it take for all the water to boil away, given that the coefficient of kinetic friction between the road and the box is mu? Neglect dissipation; take the boiling point of water to occur at temperature T_b, the specific heat of water to be c_w, specific heat of the box's metal to be c_m, and water's latent heat of vaporization to be L_v. 5. A weird alien race has built two concentric spherical metal shells around a star. The radius of the star is R and its temperature is T; the radius of the first shell is 2R and of the second is 3R. Take the emissivity of the star to be 1, and the emissivity and absorptivity of each shell to be equal. Find the temperature of the first shell. ...
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