VIPSolutionsgive answer in 2 step with explanation at the end of each step and final answer at the end:Thermodynamics in Mechanical Engineering Numerical Problems An engine receives 9000 J of heat from the source and rejects 6300 J to the sink. Calculate the thermal efficiency of the engine.
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give answer in 2 step with explanation at the end of each step and final answer at the end:Thermodynamics in Mechanical Engineering Numerical Problems An engine receives 9000 J of heat from the source and rejects 6300 J to the sink. Calculate the thermal efficiency of the engine.
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Asked by: Rahul
Created at: 2026-01-23 03:13:32
Asked by: Rahul
Created at: 2026-01-23 03:13:32
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# Step 1: Write the Formula and Substitute Values
The thermal efficiency (\(\eta\)) of a heat engine is given by:
\[
\eta = \frac{Q_1 - Q_2}{Q_1}
\]
where
\(Q_1\) = heat absorbed from the source = 900 J
\(Q_2\) = heat rejected to the sink = 630 J
Substituting the values:
\[
\eta = \frac{900 - 630}{900}
\]
**Explanation:**
This step uses the definition of thermal efficiency, which is the ratio of work output to heat supplied.
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# Step 2: Calculate the Efficiency
\[
\eta = \frac{270}{900} = .3
\]
Converting to percentage:
\[
\eta = .3 \times 100 = 30\%
\]
**Explanation:**
This step subtracts the rejected heat from the supplied heat to get the net work output, divides by the supplied heat, and converts the result to a percentage.
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# Final Answer
**The thermal efficiency of the engine is \(30\%\).**
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