Difference between amount of work done by system and amount of heat transfer initial stage is
Answers
Consider a gas in a cylinder at room temperature (T = 293 K), with a volume of 0.065 m3. The gas is confined by a piston with a weight of 100 N and an area of 0.65 m2. The pressure above the piston is atmospheric pressure.
(a) What is the pressure of the gas?
This can be determined from a free-body diagram of the piston. The weight of the piston acts down, and the atmosphere exerts a downward force as well, coming from force = pressure x area. These two forces are balanced by the upward force coming from the gas pressure. The piston is in equilibrium, so the forces balance. Therefore:

Solving for the pressure of the gas gives:

The pressure in the gas isn't much bigger than atmospheric pressure, just enough to support the weight of the piston.
(b) The gas is heated, expanding it and moving the piston up. If the volume occupied by the gas doubles, how much work has the gas done?
An assumption to make here is that the pressure is constant. Once the gas has expanded, the pressure will certainly be the same as before because the same free-body diagram applies. As long as the expansion takes place slowly, it is reasonable to assume that the pressure is constant.
If the volume has doubled, then, and the pressure has remained the same, the ideal gas law tells us that the temperature must have doubled too.
The work done by the gas can be determined by working out the force applied by the gas and calculating the distance. However, the force applied by the gas is the pressure times the area, so:
W = F s = P A s
and the area multiplied by the distance is a volume, specifically the change in volume of the gas. So, at constant pressure, work is just the pressure multiplied by the change in volume:

This is positive because the force and the distance moved are in the same direction, so this is work done by the gas.