Chapter 24, Problem 58A

A heat engine operates between $T_{hot}=750°C$ and $T_{cold}=35°C$. Michael says that the theoretical maximum efficiency is about 70%. Do you agree? If so, show why. If not, show why not.

To determine

To explain: Whether person M is correct or not.

Answer to Problem 58A

Yes, agreed with person M. The theoretical maximum efficiency is 70%.

Explanation of Solution

Given:

A heat engine operates between ${\text{T}}_{\text{hot}}=750°\text{C}$ and ${\text{T}}_{\text{cold}}=35°\text{C}$ .

Formula used:

The efficiency of a heat engine is calculated as:

  ${\eta }_{\text{theoritical}}=\frac{{\text{T}}_{\text{hot}}{\text{-T}}_{\text{cold}}}{{\text{T}}_{\text{hot}}}$

Calculation:

Temperature in kelvin is,

  $\begin{array}{c}{\text{T}}_{\text{hot}}=750°\text{C}\\ =\text{(750+273) K}\\ =\text{1023 K}\end{array}$

  $\begin{array}{c}{\text{T}}_{\text{cold}}=35°\text{C}\\ =\text{(35+273) K}\\ =\text{308 K}\end{array}$

The theoretical maximum efficiency of a heat engine is calculated as:

  $\begin{array}{l}{\eta }_{\text{theoritical}}=\frac{{\text{T}}_{\text{hot}}{\text{-T}}_{\text{cold}}}{{\text{T}}_{\text{hot}}}=\frac{1023-308}{1023}\\ {\eta }_{\text{theoritical}}=0.6989\approx 0.70=70\%\end{array}$

Conclusion:

Thus, results obtained by calculation and those predicted by M matches which is $70\%$ .