12. An ideal gas is allowed to expand adiabatically. Assume the process is reversible. The change in entropy is: (A)0 (B)nR ln(V₂/V₁) (C)nR ln(T₂/T₁) (D)kn ln(V₂/V₁) (E)kn ln(T₂/T₁)

5. A solid wheel with mass M, radius R, and rotational inertia MR²/2, rolls without sliding on a horizontal surface. A horizontal force F is applied to the axle and the center of mass has an acceleration a. The magnitudes of the applied force F and the frictional force f of the surface, respectively, are: (A)F = Ma, f = 0 (B)F = Ma, f = Ma/2 (C)F = 2Ma, f = Ma (D)F = 2Ma, f = Ma/2 (E)F = 3Ma/2, f = Ma/2

12. An ideal gas is allowed to expand adiabatically. Assume the process is reversible. The change in entropy is:
(A)0
(B)nR ln(V₂/V₁)
(C)nR ln(T₂/T₁)
(D)kn ln(V₂/V₁)
(E)kn ln(T₂/T₁)

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