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  • Question : Heat Engine Efficiency and Heat Output A heat engine absorbs 3000 J of heat from a high-temperature reservoir and releases 1500 J of heat to a low-tempera

Question : Heat Engine Efficiency and Heat Output

A heat engine absorbs 3000 J of heat from a high-temperature reservoir and releases 1500 J of heat to a low-temperature reservoir during each cycle. Calculate the efficiency of the heat engine and the work done by the engine during each cycle.

Option: 1

1500 J


Option: 2

1600 J


Option: 3

1800 J


Option: 4

2000 J


Answers (1)

best_answer

The efficiency \mathrm{\eta } of a heat engine is given by the formula:

\mathrm{\eta=\frac{W}{Q_h}=1-\frac{Q_c}{Q_h} }

Given

\mathrm{Q_h=3000 \mathrm{~J}} (heat absorbed from high-temperature reservoir)

\mathrm{Q_c=1500 \mathrm{~J}} (heat released to low-temperature reservoir)

Calculate the efficiency:

\mathrm{\begin{aligned} & \eta=1-\frac{Q_c}{Q_h} \\ & \eta=1-\frac{1500 \mathrm{~J}}{3000 \mathrm{~J}} \\ & \eta=0.5 \end{aligned}}

The work (W) done by the engine can be calculated using the work-efficiency
relationship:

\mathrm{W=\eta \cdot Q_h}

Substitute the values:

\mathrm{\begin{aligned} & W=(0.5) \cdot 3000 \mathrm{~J} \\ & W=1500 \mathrm{~J} \end{aligned}}

 

 

 

 

Posted by

Suraj Bhandari

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