91Ó°ÊÓ

The heat engine can be used to convert an amount of heat into an amount of mechanical energy.

This engine receives some amount of heat from a high-temperature source. It utilizes some part of the heat for work. Thereafter, it rejects the remaining (non-utilized) part of the energy into the low-temperature source.

The given data can be listed below as:

• The heat rejected by the heat engine is\({Q_{\rm{L}}} = 8200{\rm{ J}}\).
• The work done by the heat engine is \(W = 2600{\rm{ J}}\).

The work done by the heat engine can be expressed as:

\(\begin{aligned}{c}W &= {Q_{\rm{H}}} - {Q_{\rm{L}}}\\{Q_{\rm{H}}} &= W + {Q_{\rm{L}}}\end{aligned}\)

Here,\({Q_{\rm{H}}}\)is the heat added or supplied to the heat engine.

The efficiency of the heat engine can be expressed as:

\(\begin{aligned}{c}e &= \left( {\frac{W}{{{Q_{\rm{H}}}}}} \right)\\e &= \left( {\frac{W}{{W + {Q_{\rm{L}}}}}} \right)\end{aligned}\)

Substitute the values in the above equation.

\(\begin{aligned}{c}e &= \left( {\frac{{2600{\rm{ J}}}}{{2600{\rm{ J}} + 8200{\rm{ J}}}}} \right)\\e &= 0.2407\\e &= 0.2407 \times 100\% \\e &= 24.07\% \end{aligned}\)

Thus, the efficiency of the heat engine is \(24.07\% \).