JEE Mains · Physics · STD 11 - Thermodynamics
- JEE Mains 2022
- Hard
- MCQ
A Carnot engine whose heat \(\operatorname{sinks}\) at \(27\,^{\circ} C\), has an efficiency of \(25 \%\). By how many degrees should the temperature of the source be changed to increase the efficiency by \(100 \%\) of the original efficiency \(?\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) Increase by \(200\,^{\circ} C\)
Step-by-step Solution
Detailed explanation
\(1-\frac{300}{ T }=0\)
\(\frac{300}{ T }=0.75\)
\(1-\frac{300}{ T }=0\)
\(\frac{300}{ T }=0.75\)
\(T =400 K\)
If efficiency increased by \(\,100 \%\) then new efficiency \(\Rightarrow n ^{\prime}=50 \%\)
\(1-\frac{300}{T^{\prime}}=0.5\)
\(T^{\prime}=600 \,K\)
Increase in temp \(=600-400\)
\(=200\, K \text { or } 200^{\circ} C\)
\(T =400\, K\)
If efficiency increased by \(100 \%\,\) then new efficiency \(\Rightarrow n ^{\prime}=50 \%\)
\(1-\frac{300}{T^{\prime}}=0.5\)
\(T^{\prime}=600\,K\)
Increase in temp \(=600-400\)
\(=200 K \text { or } 200\,^{\circ} C\)
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