A diatomic ideal gas is used in a Carnot engine as the working substance

• 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 PV^γ = constant

TV^γ-1 = constant

T_bV_b^γ-1 = T_cV_c^γ-1

T_b/V_c = [V_c/V_b]^γ-1 = [32V/V]^(7/5)-1 

= [2⁵]^2/5

T_b = 4T_c = 4

i.e. 1 - (T_c/T_b) = 1 - (1/4) = 3/4

The correct option is B.