300 cal. of heat is given to a heat engine and it rejects 225 cal. of heat. If source temperature is $227^{\circ} \mathrm{C}$, then the temperature of sink will be ____ $^{\circ}\mathrm{C}$.

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Heat & Thermodynamics

300 cal. of heat is given to a heat engine and it rejects 225 cal. of heat. If source temperature is

22 7^{\circ} C

, then the temperature of sink will be ____

^{\circ} C

Answer: 102

Solution

For a heat engine operating between two reservoirs, the efficiency relation gives:

\frac{Q _{2}}{Q _{1}} = \frac{T _{2}}{T _{1}}

where

Q_{1} = 300

cal (heat absorbed),

Q_{2} = 225

cal (heat rejected), and

T_{1} = 227 + 273 = 500

K.

Substituting:

\frac{225}{300} = \frac{T _{2}}{500}

T_{2} = \frac{225 \times 500}{300} = 375 K

Converting to Celsius:

T_{2} = 375 - 273 = 10 2^{\circ} C

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Integer answer

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