Question

n mole of a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes:

A `→` B: Isothermal expansion at temperature T so that the volume is doubled from V₁ to V₂ = 2V₁ and pressure changes from P₁ to P₂.

B `→` C: Isobaric compression at pressure P₂ to initial volume V₁.

C `→` A: Isochoric change leading to change of pressure from P₂ to P₁.

Total workdone in the complete cycle ABCA is ______.

पर्याय

• 0

• `"nRT"("IN"2+1/2)`

• nRT In 2

• `"nRT"("IN"2-1/2)`

Answer 1

Total workdone in the complete cycle ABCA is `bb("nRT"("IN"2-1/2))`.

Explanation:

As A `→` B is isothermal process

⇒ `"W"_("AB") = "nRT"  "In" ("V"_2/"V"_1)`

= `"nRT"  "In" ((2"V"_1)/"V"_1)`

= nRT In (2)

As B `→` C is isobaric process

⇒  W_BC = P Δ V

= nR Δ T

= nR`("T"/2-"T")`

= `-"nR""T"/2`

As C `→` A is isochoric process

⇒  W_CA = 0

Work done by gas in complete cycle ABCA

W = W_AB +W_BC + W_CA 

= nRT In (2) + `(-"nR""T"/2)` + 0

W = nRT `("In" (2) -1/2)`