A diatomic ideal gas is used in Carnot's engine as working substance. During adiabatic expansion of the cycle, if the volume of the gas increases from V to 32 ~V , then the efficiency of the engine is

Step-by-step solution

Given, volume at C=V and volume at D=32 ~V For adiabatic expansion C D , aligned T_C V_C^ -1 & =T_D V_D^ -1 T_C T_D = ( V_D V_C )^ -1 & = ( 32 V V )^ -1 =32^ 7 5 -1 T_C T_D & =(32)^ 2 5 =4 aligned Now, efficiency of Carnot's cycle, =1- T_D T_C =1- 1 4 = 3 4 =0 75