Question
A heat engine transfers 1500 J of heat from a hot reservoir to a cold reservoir in order to do 800 J of work. What is the efficiency of this heat engine?
Answers below:
32%
67%
45%
53%
Answers below:
32%
67%
45%
53%
Answers
GPT-4o mini
The efficiency of a heat engine can be calculated using the formula:
\[
\text{Efficiency} (\eta) = \frac{\text{Work output}}{\text{Heat input}} \times 100\%
\]
In this case, the work output is 800 J, and the heat input from the hot reservoir is 1500 J. Now we can substitute these values into the formula:
\[
\eta = \frac{800 \, \text{J}}{1500 \, \text{J}} \times 100\%
\]
Calculating the fraction first:
\[
\frac{800}{1500} = \frac{8}{15} \approx 0.5333
\]
Now converting this to a percentage:
\[
\eta \approx 0.5333 \times 100\% \approx 53.33\%
\]
Rounding this to the nearest whole number gives us an efficiency of approximately 53%.
Thus, the efficiency of the heat engine is **53%**.
\[
\text{Efficiency} (\eta) = \frac{\text{Work output}}{\text{Heat input}} \times 100\%
\]
In this case, the work output is 800 J, and the heat input from the hot reservoir is 1500 J. Now we can substitute these values into the formula:
\[
\eta = \frac{800 \, \text{J}}{1500 \, \text{J}} \times 100\%
\]
Calculating the fraction first:
\[
\frac{800}{1500} = \frac{8}{15} \approx 0.5333
\]
Now converting this to a percentage:
\[
\eta \approx 0.5333 \times 100\% \approx 53.33\%
\]
Rounding this to the nearest whole number gives us an efficiency of approximately 53%.
Thus, the efficiency of the heat engine is **53%**.