# Evaluation of work in thermodynamics

Inside a cylinder with a sliding piston, n mole of monoatomic ideal gas at temperature TA occupy a volume VA at pressure PA, in equilibrium. The piston is expanded very slowly, turning the pressure in such a way that the product V⋅P2 remains constant till the volume VB .

I have to evaluate the work in the transformation from A to B:
VB = 4 VA
PA and VA are known

wAB = ∫ P⋅dV =

My question is:
- Which value of Pressure shall I insert instead of P considering the fact that it isn't constant during the transformation?

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Chestermiller
Mentor
If VP2 remains constant, it must be equal to VP2 in state A. Can you write an equation to express this in terms of PA and VA?

Chet

Doc Al
Mentor
My question is:
- Which value of Pressure shall I insert instead of P considering the fact that it isn't constant during the transformation?
Express P as a function of V.

VA⋅PA2=VB⋅PB2
Then
PA=(VB½⋅PB)/VA½
and then I substitute in the integral:
∫ (VB½⋅PB)/VA½ dV

is it ?

Chestermiller
Mentor
VA⋅PA2=VB⋅PB2
Then
PA=(VB½⋅PB)/VA½
and then I substitute in the integral:
∫ (VB½⋅PB)/VA½ dV

is it ?
Not exactly. VP2=VAPA2

Solve for P and then integrate PdV between VA and VB.

Aw ok! now i get it.