Two Carnot engines are cascaded between reservoirs at 8 K and 2 K, with intermediate temperature T. If their efficiencies are equal, find T (K).
Physics · Mixed Chapter
JEE Main Practice

Question

Two Carnot engines are cascaded between reservoirs at 8 K and 2 K, with intermediate temperature T. If their efficiencies are equal, find T (K).

G1 Physics · Accepted Answer

Step 1: For first engine η₁=1−T/8. Step 2: For second engine η₂=1−2/T. Step 3: Equality η₁=η₂ gives T/8=2/T⇒T²=16. Step 4: T=4 K (positive temperature).