Answer:
The work done on the gas is equal to the area under the curve pv diagram w = area of triangle = 1/2 (base)(height) = 1/2 (BC)(Ac) = 1/2 (3v - v)(3p - p) = 1/2 (9 vp - 3 vp - 3vp + vp) = 4 vp/2 W = 2 vp
Check attachment for the diagrammatic representation
In collision type of problems since momentum is always conserved
we can say
So here along with this equation we also required one more equation for the restitution coefficient
so above two equations are required to find the velocity after collision
here the change in velocity occurs due to the contact force while they contact in each other
so this is the impulse of collision while they are in contact with each other while in collision which changes the velocity of two colliding objects