Question

Derive an expression for work done in isothermal reversible expression process when pressure and volume are known for initial and final state

Answer 1

Answer:

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Answer 2

Answer:

Solution:-

Let us consider n moles of ideal gas enclosed in a cylinder fitted with a weightless and frictionless piston. The work of expansion for a small change of volume dV against the external pressure P is given by-

dW=−PdV

∴ Total work done when the gas expands from initial volume V

1

2

, will be-

W=−∫

V

1

V

2

PdV

For an ideal gas,

PV=nRT

⇒P=

V

nRT

Therefore,

W=−∫

V

1

V

2

V

nRT

dV

For isothermal expansion, T is constant.

Therefore,

At constant temperature,

Equation (1)&(2) are the expression for the work obtained in an isothermal reversible expansion of an ideal gas.