110年 - 110 國立政治大學_碩士班暨碩士在職專班招生考試_ 應用物理研究所:普通物理#102199

3.A heat engine operates between two reservoirs at T₂ = 500 K and T₁ = 300 K. It takes in 1000 J of energy from the higher-temperature reservoir and performs 250 J of work in one cycle. Find (a) the entropy change of the Universe △S_U, for this process and (b) the work Wthat could have been done by an ideal Carnot engine operating between these two reservoirs. (c) Show that the difference between the amounts of work done in parts (a) and (b) is T₁ △S_U. (15%)

5.A rectangular loop with width L and a slide wire of mass m are as shown in the figure. A uniform magnetic field B is directed perpendicular to the plane of the loop into the plane of the figure. The slide wire is given an initial speed of U₀at t = 0 and then released. There is no friction between the slide wire and the loop, and the resistance of the loop is negligible in comparison to the resistance R of the slide wire.(a) Obtain an expression for F, the magnitude of the force exerted on the slide wire while it is moving at speed u. (b) Find the speed u(t) and displacement x(V) in terms of B, I, m, R and u₀. (c) Find the maximum distance the slide wire moves. (d) What is the total energy consumed by the resistance R? (20%)

6. A source of sinusoidal electromagnetic waves radiates uniformly in all directions with an average power of 50.0 kW and frequency 100 MHz. At a distance 10.0 km from the source there is a circular loop of wire with diameter 0.200 m. Calculate (a) the intensity of the electromagnetic wave and (b) the amplitudes of the electric and magnetic fields at the location of the loop. (c) If the loop is perpendicular to the direction of the radiation's magnetic field, what is the maximum electromotive force induced in the wire? (20%)