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22/01/2022 1:49 pm
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A reversible engine has an efficiency of 1/4. If the temperature of the sink is reduced by 58°C, its efficiency becomes double. Calculate the temperature of the sink
(1) 174°C
(2) 280°C
(3) 180.4°C
(4) 382°C
1 Answer
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22/01/2022 1:55 pm
Correct answer: (1) 174°C
Explanation:
T2 = sink temperature
η = 1 - \(\frac{T_2}{T_1}\)
\(\frac{1}{4}\) = 1 - \(\frac{T_2}{T_1}\)
\(\frac{T_2}{T_1}\) = \(\frac{3}{4}\) .....(i)
\(\frac{1}{2}\) = 1 - \(\frac{T_2 - 58}{T_1}\)
\(\frac{T_2}{T_1}\) - \(\frac{58}{T_1}\) = \(\frac{1}{2}\)
\(\frac{3}{4}\) = \(\frac{58}{T_1}\) + \(\frac{1}{2}\)
\(\frac{1}{4}\) = \(\frac{58}{T_1}\) ⇒ T1 = 232
T2 = \(\frac{3}{4}\) x 232
T2 = 174K