7. One mole of an ideal monatomic gas is taken around the reversible cycle as shown in the figure. The isothermals are at 500 K and 300 K. Find the efficiency of the engine.

3. A force varies as = xy²î. What is the work done by the force along the paths OB? 

4. Same conditions as the above question, does the force = xy²î satisfy the criterion for being conservative (yes or no)? ______

5. A particle of mass m travels in a horizontal circle on a frictionless table. The centripetal force is provided by a string, attached to two bodies of equal mass M, which passes through a hole in the table. The radius of the circle is r. If one of the hanging masses is removed, the new radius will be ______

6. Water fills a length L of a U tube. The water is slightly displaced and then allowed to move freely. The liquid will then execute a simple harmonic motion. What is the angular frequency (ω) of the oscillation? 

8. Same conditions as the above question, find the total entropy change of the heat engine from b to a through the process of b→ c → d → a.

9. The figure shows three identical conducting spheres with these initial charges: A, -12Q, B, +8Q, C, 0. Here is the procedure for connecting and then disconnecting spheres with wire: Step 1: connect A and C and then disconnect； Step 2: connect B and C and then disconnect, moving C far away； Step 3: connect A and B and then disconnect. A and B have a center-to-center separation r. What is the magnitude of the final force between those two spheres? Answer by writing what goes in the blank in this equation: F = _kQ² / r².

10. The figure shows three situations in which the same charged particle is surrounded by a concentric Gaussian sphere. (1) sphere has radius R (2) sphere has radius 2R  (3) sphere has radius 2R and also surrounds a neutral metal spherical shell Rank the three situations according to the magnitude of the electric flux through the surface of the Gaussian sphere, greatest first. NOTE:請依序排列,並加註大於、小於、或等於符號(＞, ＜, or =)。

11. In the following figure, we have V = 9.0 V, C2 = 3.0 µF, and C4 = 4.0 µF, and all the capacitors are initially uncharged. When switch S is closed, a total charge of 20 µC passes through point a and a total charge of 8.0 µC passes through point b. What is capacitance C3 (uF)? 

12. An alpha particle (q = +2e, m = ) travels in a circular path of radius 4.50 cm in a uniform magnetic field with B = 1.20 T. Through what potential difference (volts) was it accelerated (from rest) to have the kinetic energy required for this path?

13. The figure shows a conducting bar sliding at speed along a wire in the shape of "U" through a uniform magnetic field that is perpendicular to the wire and bar: speed = 3.0 m/s, left-right width L = 5.0 m, induced emf = 360 V counterclockwise. What is the magnitude (T) of the magnetic field?