Three Carnot engines operate in series between a heat source at temperature T₁ and heat sink at a temperature T₄ . There are two other reservoirs at temperatures T₂ and T₃ . The three engines are equally efficient, if (given that, .T₁>T₂>T₃>T₄ )

Step-by-step solution

Given, efficiencies ₁= ₂= ₃= and temperature, T₁>T₂>T₃>T₄ As we know that, in case of Carnot engine, aligned & Efficiency ( )=1- T_ sink T_ source & ₁= =1- T₂ T₁ & T₂=(1- ) T₁ & Similarly, T₃=(1- ) T₂ & T₄=(1- ) T₃ & aligned Now, by using Eqs. (i), (ii) and (iii), we get aligned (T₁^2 T₄ )^ 1 / 3 & = [ ( T₂ 1- )^2 (1- ) T₃ ]^ 1 / 3 & = [ T₂^2 (1- ) T₃ ]^ 1 / 3 & = [ ( T₂^2 1- )(1- ) T₂ ]^ 1 / 3 & = [T₂^3 ]^ 1 / 3 =T₂ aligned Again, by using Eqs. (i), (ii) and (iii), we get aligned (T₁ T₄^2 )^ 1 / 3 & = ( T₂ 1- ) [(