KCET · Physics · Thermodynamics
A Carnot's engine operates with source at \(127^{\circ} \mathrm{C}\) and sink at \(27^{\circ} \mathrm{C}\). If the source supplies \(40 \mathrm{~kJ}\) of heat energy, the work done by the engine is
- A \(30 \mathrm{~kJ}\)
- B \(10 \mathrm{~kJ}\)
- C \(4 \mathrm{~kJ}\)
- D \(1 \mathrm{~kJ}\)
Answer & Solution
Correct Answer
(B) \(10 \mathrm{~kJ}\)
Step-by-step Solution
Detailed explanation
Efficiency \(\eta=1-\frac{T_{2}}{T_{1}}\)
\(=1-\frac{(273+27)}{(273+127)}=1-\frac{300}{400}=\frac{1}{4}\)
\(\eta =\frac{\text { Work done }}{\text { Heat supplied }}\)
\(\frac{1}{4} =\frac{W}{40} \Rightarrow W=10 \mathrm{~kJ}\)
\(=1-\frac{(273+27)}{(273+127)}=1-\frac{300}{400}=\frac{1}{4}\)
\(\eta =\frac{\text { Work done }}{\text { Heat supplied }}\)
\(\frac{1}{4} =\frac{W}{40} \Rightarrow W=10 \mathrm{~kJ}\)
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