Answer:
The efficiency of the engine is 75% under given conditions.
Explanation:
Efficiency is defined as the ratio of work done by the engine to the total heat supplied to a heat engine. We know work done by the heat engine be difference between total heat supplied [tex]\left(Q_{h}\right)[/tex] by total heat utilized [tex]\left(Q_{c}\right)[/tex]. We can derive formula for efficiency by considering the above factors, [tex]\text { efficiency }=\frac{\text { work done }}{\text { heat suplied }}=\frac{Q_{h}-Q_{c}}{Q_{h}}=1-\frac{Q_{c}}{Q_{h}}=1-\frac{T_{1}}{T_{2}} \therefore \text { efficiency }=1-\frac{T_{1}}{T_{2}}[/tex]
Now consider a heat engine is at a temperature of 500K and the heat produced by the engine released to the surroundings at a temperature of 125K. The efficiency is calculated by using the above formula, [tex]\text { efficiency }=1-\frac{T_{1}}{T_{2}}=1-\frac{125}{500}=1-0.25=0.75[/tex]
∴ Efficiency of the engine is 75%
