Question

. 23) Deriv
e an expression for maximum work.​

Answer 1

⬆️2 ⬆️3 ⬆️1

Answer:

Explanation:

(1)

Consider n moles of an ideal gas enclosed in an ideal cylinder fitted with a massless and frictionless movable rigid piston. Let V be the volume of the gas at a pressure P and a temperature T.

If in an infinitesimal change pressure changes from P to P – dP and volume increases from V to V + dV. Then the work obtained is, dW = - (P-dP) dV

= -PdV + dPdV

Since dP.dV is negligibly small relative to PdV

  dW = -PdV

Let the state of the system change from A(P1, L1) to B (P2, V2) isothermally and reversibly, at temperature T involving number of infinitesimal steps.

A -> B (Upon T) A(P1,V1) , B (P2,V2)

Then the total work or maximum work in the process is obtained by integrating above equation.

(2)

At constant temperature,

(3)

where n, P, V and T represent number of moles, pressure, volume and temperature respectively. For the process,

ΔU = 0, ΔH = 0.

The heat absorbed in reversible manner Qrev, is completely converted into work.

Qrev = -Wmax.

Hence work obtained is maximum.