Question
Derive an expression for pressure-volume work (PV – work).
Solution
Let us consider a gas enclosed in a cylinder fitted with a frictionless piston having an area of cross-section equal to ‘a’. Let the gas expand against the external pressure P facing the piston to move through a small distance d. Then work of expansion is given by,
During expansion, work is done by the system and ∆V(V2 – V1) is positive. Therefore, in order to satisfy the sign conventions, a negative sign is put in the expression for work.
During compression, Work is done on the system. ∆V(V2 – V1) for compression is negative. Therefore work, as obtained from the above expression, comes out to be positive and satisfies the conventions.
The general expression for all types of PV-work is given by
During expansion, work is done by the system and ∆V(V2 – V1) is positive. Therefore, in order to satisfy the sign conventions, a negative sign is put in the expression for work.
During compression, Work is done on the system. ∆V(V2 – V1) for compression is negative. Therefore work, as obtained from the above expression, comes out to be positive and satisfies the conventions.
The general expression for all types of PV-work is given by
