AP Physics B Homework question.?

Question

A gas is contained in a chamber such as that in Figure 15.5. Suppose the region outside the chamber is evacuated and the total mass of the block and the movable piston is 120 kg. When 2030 J of heat flows into the gas, the internal energy of the gas increases by 1745 J. What is the distance s through which the piston rises?
http://www.webassign.net/CJ/15_05.gif

Answer 1

Basic conservation of energy problem. 2030 J of heat went in, only 1745 J of which contributed to the internal energy of the gas, so this means 2030 J - 1745 J or 285 J of work was done on the piston and block. Let E be the gravitational potential energy of the block and piston, h be the height of the block (thus s=Δh, but I'll use Δh to avoid confusion with seconds), a_g be the acceleration due to gravity, and m be the mass of the piston and block. Then:
ΔE=m*a_g*Δh
285 J = 120 kg * 9.81 m/s² * Δh
Δh = 285 J / (120 kg * 9.81 m/s²) = 0.24 meters

Answer 2

The answer given by Pascal is fully correct. Here the work done by the gas (due to pressure) thrust is against the force of gravity (due to earth). Hence the work done is mgh. Here we assume that there is no frictional force between piston and the cylinder, and the piston is going up infinitely slowly with almost no velocity at all so that the change in its kinetic energy is also zero.

Then you may also be wondering that if the outside is evacuated why does not gas expand against vacuum. It does expand to such a pressure and volume so that thrust (pressure x area of piston) becomes equal to the force mg due to earth. Thus you can see that the usual formula p x change of volume also gives you the same answer. Change of volume being equal to (change of height x area of the piston).