A Carnot engine operating between two reservoirs has efficiency . When the temperature of the cold reservoir is raised by , its efficiency decreases to . The value of , if the temperature of the hot reservoir is , will be [2023]

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Solution

Q.
A Carnot engine operating between two reservoirs has efficiency $\frac{1}{3}$ . When the temperature of the cold reservoir is raised by $x$ , its efficiency decreases to $\frac{1}{6}$ . The value of $x$ , if the temperature of the hot reservoir is $99 ° C$ , will be [2023]

1 16.5 K

2 33 K

3 66 K

4 62 K

Ans.
(4)

$T_{H} = 99 ° C = 99 + 273 = 372 K$

$1 - \frac{T_{H}}{T_{C}} = \frac{1}{3}$

$\frac{T_{C}}{T_{H}} = \frac{2}{3} ...(1)$

$\Rightarrow T_{C} = \frac{2}{3} \times 372 = 2 \times 124 = 248 K$

$1 - \frac{T_{C} + X}{T_{H}} = \frac{1}{6}$

$\Rightarrow \frac{5}{6} = \frac{248 + X}{372}$

$248 + X = 5 \times 62$

$\Rightarrow X = 310 - 248 = 62 K$

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