 

PRESSUREVOLUME WORK  
Consider a cylinder fitted with a frictionless and weightless nonconducting piston of area of cross section “A” . An ideal gas is enclosed in the cylinder. Let the volume of gas at initial state is “V_{1}“. An external pressure “P“is exerted on the piston. 
 
If we supply “q” amount of heat to the system then it will increase its internal energy by DE. “After a certain limit gas exerts pressure on the piston . If piston is free to move, it will be displaced by “h” & volume of system increases from V_{1} to V_{2}.
We know that pressure is the force per unit area i.e.  P = F/A OR F = PA …….. (i)  We also know that the work done by the gas on the piston is given by: 
 DW = F d  Where d = displacement of piston = h  Putting the value of F and d ,we get  DW = (PA) h  OR DW = P (Ah)  But Ah = change or increase in volume = DV  Hence  DW = P DV   
  
