Calculate the work done by the torque.

Explanation

(i)The essential condition of expansion or compression of a system is there should be difference between external pressure `(P_"ext")` and internal pressure `(P_"int")`
(ii)If the volume of the system is increased against the external pressure, the work is done by the system. By convention work done by the system is given a negative sign (-w).
(iii) If the volume of the system decreased, the work is done on the system. By convention work done on the system is given positive sign (+W).
(iv) For understanding pressure-volume work, let us consider a cylinder which contains one mole of an ideal gas fitted with a frictionless piston. Total volume of the gas is V and pressure of the gas inside is `P _"int"`.
(v)If external pressure is `P_"ext"` which is greater than `P_"int"` Piston is moved i want till the pressure inside becomes equal to `P_"ext"`. It is achieved in a single step and the final volume be `V_f`.
(vi)During this compression, piston moves a distance (x) and is cross-sectional area of the piston is A, then,
Change in volume = `xA =DeltaV =V_f -V_i` ...(1)
`P_"ext"="Force(F)"/"Area (A)"`....(2)
`therefore F=P_"ext" A`
(vii) If work is done by the system by pushing out the piston against external pressure `(P_"ext")`, then according to the equation,
-w=F. x ...(3)
-w=`P_"ext".A . x`...(4)
-w=`P_"ext".DeltaV`...(5)
`-w=P_"ext" (V_f-V_i)` ....(6)
Simply `w=-P DeltaV`...(7)
(viii)From the above equation , we can predict the sign of work (w).
(ix) During expansion, work is done by the system , since `V_f > V_i` , the sign obtained for work will be negative.
(x)During compression, work is done on the system, since `V_f lt V_i` , the sign obtained for work will be positive.