40. An ideal gas undergoes a Carnot cycle. If the volume of the gas doubles during the isothermal expansion, how does the magnitude of the work done on the gas during the isothermal compression compare to the magnitude of the work done by the gas during the isothermal expansion?
(A) The work of compression is greater.
(B) The work of expansion is greater.
(C) Both are equal.
(D) It depends on the temperature ratio of the high- and low-temperature reservoirs.

41. One mole of a monatomic ideal gas is mixed with one mole of a diatomic ideal gas. Assuming no chemical reaction occurs and they reach thermal equilibrium, what is the molar specific heat at constant volume of this gas mixture? (assume R is the ideal gas constant) (A) 1.5 R (B) 2.0 R (C) 2.5 R (D) 3.5 R

42. The current density in a particle beam with circular cross section of radius a points along the beam axis with a magnitude that decreases linearly from J0 at the center (r = 0) to half that value at the edge (r = a). What is the total current in the beam? (A) (B) (C) (D)(E)

43. A disk of radius a carries uniform surface charge density σand rotates with angular speed ω about the disk axis. What is the magnetic field at the disk center? (μ0 is the magnetic constant.) (A) μ0σωa (B)μ0πσa2 (C) μ0πσa2(D) μ0σωa2(E) μ0σωa

44. A long, straight coaxial cable consists of two thin, tubular conductors, the inner of radius a and the outer radius b. Current I flows out along one conductor and back along the other. What is the self-inductance per unit length of the cable? (μ0 is the magnetic constant.) (A) (B) (C) (D) (E)

45. The figure shows light passing through a spherical raindrop, undergoing two refractions and total internal reflection. What is the correct relation among angleΦ in the figure, the incident angleθ, and the refractive index of the raindrop n? (A)Φ = 4 sin−1 (sin 2θ /n) − θ (B) Φ= 2 sin−1 (sin 2θ /n) − 2θ (C) Φ = 4 sin−1 (sin θ /n) −θ(D) Φ = 4 sin−1 (sinθ /n) − 2θ(E) Φ= 2 sin−1 (sin θ /n) − 2θ

46. Diffraction imposes a fundamental limit on the ability of optical systems to distinguish closely spaced objects. In general, two peaks are barely distinguishable if the central maximum of one coincides with the first minimum of the other. The two sources become just barely resolved when the Rayleigh criterion is met. Accordingly, what is the Rayleigh criterion for single-slit diffraction? Assume a is the slit width andθmin is the minimum angle separation in the figure. (A) (B) (C) (D)(E)

47. In 1900, the German physicist Max Planck formulated an equation that fit the observed radiance curves forblackbody radiation at all wavelengths: R(λ, T) =, where ℎ is Planck’s constant, c is the speed of light, λ is wavelength, k is Boltzmann’s constant, and T is the absolute temperature. If we integrate the equation over all wavelengths to calculate the total power radiated per unit area, the Stefan-Boltzmann law for blackbody radiation can be derived. Assume A is the area of the radiating surface. Note that， where Γ(n) is the gamma function and  ζ(n) is the Riemann zeta function.For references,. What is the Stefan-Boltzmann law for blackbody radiation?(A) (B)(C) (D) (E)

48. A bullet of mass m is fired horizontally with a speed v into a stationary wooden block of mass M and becomes embedded in it. If the block is suspended by a string of length L (forming a simple pendulum system), what fraction of the initial kinetic energy is lost as mechanical energy during the moment of impact? (A) m / (m + M) (B) M / (m + M) (C) m / M (D) (M - m) / (M + m)

49. Consider a soap bubble and a liquid drop of the same radius. If both have the same surface tension γ, radius R, and external pressure P0, what is the relationship between the internal pressure of the soap bubble (Pbubble) and the internal pressure of the liquid drop (Pdrop)? (A) Pbubble ＞ Pdrop (B) Pbubble ＜ Pdrop (C) Pbubble = Pdrop (D) Cannot be compared

50. An electric diple consists of point charges ±q a distance 2a apart. The potential at an arbitrary point P can be expressed as V(P) = = , where k is the Coulomb constant, r+ is the distance to the point charge +, r− is the distance to the point charge −q. If r is the distance to the dipole center, for r ≫ a, the quantities r+, r−, and r are nearly the same as r2 ≈ r+r−. The difference between the distances from the two charges to P, that is, r− − r+, is approximately equal to 2a cos θ, where θ is the angle as shown in the figure. Eventually, the dipole potential for r ≫ a becomes V(r, θ) = . What is the electric field at an arbitrary position P for r ≫ a? Note that and are unit vectors. (A) (B)(C) (D)(E)

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