A refrigerator consumes an average 35 W power to operate between temperature $-10^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C}$. If there is no loss of energy then how much average heat per second does it transfer?

(D) $263 \mathrm{~J} / \mathrm{s}$

(A) $350 \mathrm{~J} / \mathrm{s}$

(B) $298 \mathrm{~J} / \mathrm{s}$

(C) $35 \mathrm{~J} / \mathrm{s}$

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Heat & Thermodynamics

A refrigerator consumes an average 35 W power to operate between temperature

- 1 0^{\circ} C

2 5^{\circ} C

. If there is no loss of energy then how much average heat per second does it transfer?

(A) $350 J / s$
(B) $298 J / s$
(C) $35 J / s$
(D) $263 J / s$ ✓ Correct

Answer: (D)

Solution

The cold and hot reservoirs are at

T_{C} = 263

K and

T_{H} = 298

K. With no loss of energy the refrigerator works at the ideal coefficient of performance

β = \frac{T _{C}}{T _{H} - T _{C}} = \frac{263}{298 - 263} = \frac{263}{35}

The heat drawn from the cold space per second follows from

Q_{C} = β W

with

W = 35

J per second:

Q_{C} = \frac{263}{35} \times 35 = 263 J s^{- 1}

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Single correct option

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