Evaluation of work in thermodynamics

[DottZakapa]

Inside a cylinder with a sliding piston, n mole of monoatomic ideal gas at temperature T_A occupy a volume VA at pressure P_A, 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 V_B .

I have to evaluate the work in the transformation from A to B:
V_B = 4 V_A
P_A and V_A are known

w_AB = ∫ 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?

 

[Chestermiller]

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

Chet

 

[Doc Al]

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.

 

[DottZakapa]

V_A⋅P_A²=V_B⋅P_B²
Then
P_A=(V_B^½⋅P_B)/V_A^½
and then I substitute in the integral:
∫ (V_B^½⋅P_B)/V_A^½ dV

is it ?

 

[Chestermiller]

V_A⋅P_A²=V_B⋅P_B²
Then
P_A=(V_B^½⋅P_B)/V_A^½
and then I substitute in the integral:
∫ (V_B^½⋅P_B)/V_A^½ dV

is it ?

Not exactly. VP²=V_AP_A²

Solve for P and then integrate PdV between V_A and V_B.

 

[DottZakapa]

Aw ok! now i get it.
Thank you very much for your time. Very helpful.
Have a nice day : )