P = F/A so F = PA
so W= PAs
Because s= distance and A = Area so As= V and
because Pressure from surrounding is constant so
dW= -P dV (In physics maybe dW = P dV ; up to consider from surrounding or system.) next step –>
P = n R T / V —> W = – ∫ (n R T / V) dV = – n R T ln (Vf / Vi).
integral of 1/v * dv = ln V
dln(x)/dx = 1/x
Since T is constant, Pi Vi = Pf Vf
(Vf / Vi) = (pi / pf).
W = n R T ln (Vf / Vi) = n R T ln (pi / pf)