Question

Q.1Derive the expansion for maximum work . (Maximum work obtained in isothermal , reversible process )​

Answer 1

Answer:

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 V1 to the final volume V2, will be-

W=−∫V1V2PdV

For an ideal gas,

PV=nRT

⇒P=VnRT

Therefore,

W=−∫V1V2VnRTdV

For isothermal expansion, T is constant.

Therefore,

W=−nRT∫V1V2VdV

⇒W=−nRT[lnV]V1V2

⇒W=−nRT(lnV2−lnV1)

⇒W=−nRTln(V1