A Carnot engine operating between temperatures T_1 and T_2 has efficiency 1/6 . When T_2 is lowered by 62 K , its efficiency increases to 1/3 . Then T - Physics MCQ FIITJEE AIEEE 2011 (Set Q) 2026 | ExamTest.live

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A Carnot engine operating between temperatures T_{1} and T_{2} has efficiency \frac{1}{6} . When T_{2} is lowered by 62 K, its efficiency increases to \frac{1}{3} . Then T_{1} and T_{2} are, respectively:

Solution & Step-by-step Explanation

Initial efficiency: η_{1} = 1 - \frac{T _{2}}{T _{1}} = \frac{1}{6} ⟹ \frac{T _{2}}{T _{1}} = \frac{5}{6} \dots (1) Final efficiency: η_{2} = 1 - \frac{T _{2} - 62}{T _{1}} = \frac{1}{3} ⟹ \frac{T _{2} - 62}{T _{1}} = \frac{2}{3} \dots (2) Subtracting (2) from (1): \frac{T _{2}}{T _{1}} - \frac{T _{2} - 62}{T _{1}} = \frac{5}{6} - \frac{2}{3} \frac{62}{T _{1}} = \frac{1}{6} ⟹ T_{1} = 372 K From (1): T_{2} = \frac{5}{6} T_{1} = \frac{5}{6} \times 372 = 310 K .

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A Carnot engine operating between temperatures T_{1} and T_{2} has efficiency \frac{1}{6} . When T_{2} is lowered by 62 K, its efficiency increases to \frac{1}{3} . Then T_{1} and T_{2} are, respectively:

372 K and 330 K

330 K and 268 K

310 K and 248 K

372 K and 310 K

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