What Are the Answers to These Challenging Physics Multiple Choice Questions?

[Sombra]

Physics Questions (mult choice!)

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 wavelength 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.

 

[wais]

1. The correct answer is c. 75%. The equation to use here is the Carnot efficiency formula: efficiency = (T(h)-T(c))/T(h) x 100%. When the temperature of the hot reservoir is increased to 2T(h), the efficiency becomes (2T(h)-T(c))/2T(h) x 100%, which simplifies to 75%.

2. The correct answer is d. Y to X, 100. The direction of the electric field is from positive to negative, so it goes from Y to X. The strength of the electric field can be calculated using the equation E = V/d, where V is the potential difference between X and Y and d is the distance between them. Plug in the given values, and you will get 100 V/cm.

3. The correct answer is c. 1/ square root of E(k). The de Broglie wavelength is given by the equation lamda = h/p, where h is Planck's constant and p is the momentum of the particle. Since kinetic energy is proportional to momentum, the wavelength is proportional to the inverse of the square root of kinetic energy.