(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

Suppose the speed of the ball relative to the wicket behind the bat is u.
If the bat is moving towards the ball with a speed V relative to the wicket , then the relative speed of the ball w.r.t. `Bat = (V+u)`, towards the bat.
On hitting the massive bat, the ball rebounds with the same speed `(V+u)`, away from the bat. Therefore, speed of rebounding ball relative to wicket `=V+(V+u) = 2V+u`, away from the wicket. Thus, the ball speeds up (moves faster) after the collision with the bat. for a molecule, it implies increase in temperature. Thus, cylinder acts as wicket , piston acts as bat and molecule act as ball.
(b) When gas in a cylinder is compressed by pushing in a piston, bat hits the ball, it moves faster and hence the temperature of the gas increases.
(c) When a compressed gas pushes a piston out and expand , velocity of ball decrease. hence temperature of the gas decreases.
(d) Sachin Tendulkar uses a heavy cricket bat. Therefore, on hitting with such a bat , velocity of the ball increases further. He is able to score better.