Kinetic Theory Gases

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V, the efficiency of the engine is

  1. .99
  2. .75
  3. .50
  4. .25

Answer

Since PVγ = constant

TVγ-1 = constant

TbVbγ-1 = TcVcγ-1

Tb/Vc = [Vc/Vb]γ-1 = [32V/V](7/5)-1 

= [25]2/5

Tb = 4Tc = 4

i.e. 1 - (Tc/Tb) = 1 - (1/4) = 3/4

The correct option is B.