7. A Carnot engine operated between temperatures TH and TL. What is the entropy gain per cycle? (A) 0 (B) kB N TH (C) (D) (E) kB N(TH − TL). Here kB is the Boltzmann constant, and N is the number of gas molecules.

3. A solid sphere of mass m and radius r moves along a track with a circular loop of radius R1 as shown in following picture. It is released at height h. Assuming that the track has no friction, the ball thereforeslides down without rotation. Do not ignore the finite size of the sphere, what is the minimal value of h such that the sphere remains on the track at all times? (A) 2.5R − 1.5r (B) 2R − r (C) 2.5R (D) 2R + r (E) 2R − 1.5r

7. A Carnot engine operated between temperatures T_H and T_L. What is the entropy gain per cycle?
(A) 0
(B) k_B N T_H
(C)
(D)
(E) k_B N(T_H − T_L). Here k_B is the Boltzmann constant, and N is the number of gas molecules.

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