Question

1. Each part of this question covers a key concept. Each requires at most a few sentences to answer; some are much shorter. Please be concise.

   1. (a) What does the Maxwell-Boltzmann distribution describe for a gas in thermal equi- librium? Suppose a gas in a closed cylinder is kept at constant temperature while being compressed to half its original volume. What effect does this compression have on the pressure that the gas exerts on the walls of the cylinder? What would happen if the same amount of compression occurs at a higher (but still constant) temperature?

   2. (b) Two planets have identical diameters but differ in mass by a factor of 20. Which planet has the larger escape velocity? By what factor?

   3. (c) Jeopardy Question. Give a question with the following answer: This occurs when compression due to gravity is balanced by a pressure gradient, which creates a force in the opposite direction

Answer 1

(a) This distributions describes the most probable speed of molecules in a gas. It tells us how speed is distributed and based on that we may calculate root mean square speed, peak velocity.

If we compress a gas without changing its temperature, the average kinetic energy of the gas particles stays the same. particles travel from one end of the container to the other in a shorter period of time. This means that they hit the walls more often. Any increase in the frequency of collisions with the walls must lead to an increase in the pressure of the gas.It means pressure by the gas will increase as volume becomes half.

As we increase the temperature, the speed of particles will further increase and this will lead to an increase in pressure.

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(b) We know that escape velocity is given as

v = sqrt (2GM / r)

where M is mass of planet and r is radius

Let M be the mass of one planet and m be the mass of other planet

then we have

M = 20m

Therefore, planet with mass M will have more escape velocity.

The factor will be 4.472

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(c) This is most probably "Hydrostatic Equilibrium"

The question can be "Explain the balance of forces in Hydrostatic equilibrium".