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A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by 62°C, the efficiency of the engine is doubled. The temperatures of the source and sink are
A 99°C, 37°C
B 80°C, 37°C
C 95°C, 37°C
D 90°C, 37°C

Respuesta :

Answer:   D) 90°C, 37°C

Explanation:

η = 1/6

η = 1 - (T2 / T1)

η' = 2 * η = 2 * (1 - (T2 - 62) / T1)

2 * (1 - (T2 - 62) / T1) = 1 - (T2 / T1)

2 - 2(T2 - 62) / T1 = 1 - T2 / T1

2 - 2(T2 - 62) = T1 - T2

2 - 2T2 + 124 = T1 - T2

T1 - T2 + 2T2 = 2 + 124

T1 + T2 = 126  ----(1)

T2 = T2' + 62

T1 + T2' + 62 = 126

T1 + T2' = 64  ----(2)

A) 99°C, 37°C --> 99 + 37 = 136 (Does not satisfy equation (2))

B) 80°C, 37°C --> 80 + 37 = 117 (Does not satisfy equation (2))

C) 95°C, 37°C --> 95 + 37 = 132 (Does not satisfy equation (2))

D) 90°C, 37°C --> 90 + 37 = 127 (Satisfies equation (2))

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