(a) When a molecule (or an elastic ball) hits a (massive) wall, it rebounds with the same speed. When a ball hits a massive bat held firmly, the same thing happens However, when the bat is moving towards the ball, the ball rebounds with a different speed. Does the ball move faster or slower?
(b) When gas in a cylinder is compressed by pushing in a piston. Its temperature rises. Guess at an explanation of this in terms of kinetic theory using (a) above
(c) What happens when a compressed gas pushes a piston out and expands. What would you observe?
(d) Sachin Tendulkar uses a heavy cricket bat while playing. Does it help him in any way?

Explanation

(a) Let the speed of the ball be u relative to the wicket behind the bat. If the bat is moving towards the ball with a speed V relative to the wicket, then the relative speed of the ball to bat is V + u towards the bat. When the ball rebounds (after hitting the massive bat) its speed, relative to bat, is V + u moving away from the bat. So relative to the wicket the speed of the rebounding ball is V + (V + u) = 2V + u, moving away from the wicket. So the ball speeds up after the collision with the bat. The rebound speed will be less than u if the bat is not massive. For a molecule this would imply an increase in temperature.You should be able to answer (b) (c) and (d) based on the answer to (a).
(Hint: Note the correspondence, piston`rarr`bat ,cylinder ` rarr` wicket ,molecule `rarr` ball.