Physics Questions (mult choice!!)

[Sombra]

These questions confuse me:
1. A heat engine operates in a Carnot cycle b/w two reservoirs, a hot reservoir at temperature T(h) and a cold reservoir at T(c). The efficiency of the engine is 50%. The temperature of the hot reservoir is increased to 2T(h). The efficiency of the engine now is--- a. 25% b. 33% c. 75% and d. 100%. (If you know of at least an equation I could use, it would be great. I ruled out 100% since it's not really possible, but I really don;t know)

2. Line X has a potential of +50V and line Y has a potential of +100V. The distance between X and Y is 2.0 cm. Which of the following gives the direction of the electric field and its strength? a. X to Y, 25 V/cm b. X to Y, 100 c. Y to X, 25 d. Y to X 100. (I have no idea how to approach this.)

3. The de Broglie wavelength of a particle that has kinetic energy E(k) is lamda. The wavelength lamda is proportial to: a. E(k) b. 1/E(k) c. 1/ square root of E(k) d. E(k)^2. (I said E(k) because they said that E(k) was lamda, but I don't know)

Thanks!!

[quasar987]

3. The De Broglie wavelenght is

\lambda = \frac{h}{p}

where h is a constant of proportionality and p is the momentum mv of the particle.

The problem will be solved if we can express p in terms of the kinetic energy E(k) (what is this weird notation?!)

E(k) = \frac{1}{2}mv^2 = \frac{1}{2}\frac{m^2v^2}{m} = \frac{1}{2}\frac{p^2}{m} \Leftrightarrow p^2 = 2mE(k) \Leftrightarrow p = \pm\sqrt{2mE(k)}

So

\lambda = \frac{h}{\pm\sqrt{2mE(k)}} = \frac{\pm h}{\sqrt{2m}}\frac{1}{\sqrt{E(k)}}

i.e. the answer is c.