કાર્નોટ એન્જિન \(127\,^oC\) તાપમાનવાળા ઉષ્મા પ્રાપ્તિ સ્થાનમાથી \(1000\,J\) ઉષ્માનું શોષણ કરીને ઠારણ વ્યવસ્થામાં \(600\,J\) ઉષ્મા ગુમાવે છે.એન્જિનની કાર્યક્ષમતા અને ઠારણ વ્યવસ્થાનું તાપમાન કેટલું કેટલું હશે?

A \(20\%\) અને \(- 43\,^oC\)
B \(40\%\) અને \(- 33\,^oC\)
C \(50\%\) અને \(- 20\,^oC\)
D \(70\%\) અને \(- 10\,^oC\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(40\%\) અને \(- 33\,^oC\)

Step-by-step Solution

Detailed explanation

Given: \(Q_1=1000 J\) \(Q_2=600 J\) \({T_1} = {127^ \circ }C = 400\,K\) \({T_2} = ?\) \(\eta = ?\) Efficiency of carnot engine, \(\eta = \frac{W}{Q_1} \times 100\% \) \(or,\,\,\eta = \frac{{{Q_2} - {Q_1}}}{{{Q_1}}} \times 100\% \)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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