$(a)$ 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 used a heavy cricket bat while playing. Did it help him in any way?

(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 the bat is $V+u$ towards the bat. When the ball rebounds (after hitting the massive bat),its speed relative to the 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. Thus,the ball moves faster after the collision with the bat.
$(b)$ When a piston is pushed into a cylinder,the gas molecules collide with the moving piston. Similar to the ball hitting a moving bat,the molecules rebound with a higher speed. Since the average kinetic energy of the molecules increases,the temperature of the gas rises.
$(c)$ When the gas expands by pushing the piston out,the molecules collide with a receding piston. The molecules rebound with a lower speed,resulting in a decrease in the average kinetic energy of the gas molecules. Consequently,the temperature of the gas drops.
$(d)$ Yes,using a heavy bat is advantageous. Since the bat is massive,it does not lose much speed upon collision with the ball. The ball rebounds with a higher speed $(2V+u)$,allowing the batsman to hit the ball further.