Question

What would be the efficiency of a Carnot engine operating with ${\mathbf{T}}_{\mathbf{H}}\mathbf{=}{\mathbf{T}}_{\mathbf{C}}$? What would be the efficiency if ${\mathbf{T}}_{\mathbf{C}}\mathbf{=}\mathbf{0}\mathbf{K}$and ${\mathbf{T}}_{\mathbf{H}}$were any temperature above 0K? Interpret your answers.

Short answer

The Carnot cycle would be 100% efficient.

Step-by-step solution

Step 1:Definition of Carnot engine

The Carnot engine is the most efficient engine which is theoretically possible. The efficiency depends only upon the absolute temperatures of the hot and cold heat reservoirs between which it operates.

Step 2:Efficiency of Carnot engine

If ${\mathrm{T}}_{\mathrm{H}}={\mathrm{T}}_{\mathrm{C}},\mathrm{e}=0$.

The Carnot engine cannot operate unless the two heat reservoirs are at different temperatures. If ${\mathrm{T}}_{\mathrm{C}}=0\mathrm{K},\mathrm{e}=1$. If the low temperature reservoir were at absolute zero, no waste heat ${\mathrm{Q}}_{\mathrm{C}}$would be deposited there and the Carnot cycle would be efficient.