JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Heat & Thermodynamics

A water heater of power 2000 W is used to heat water. The specific heat capacity of water is 4200 J

kg^{- 1} K^{- 1}

. The efficiency of heater is

70%

. Time required to heat 2 kg of water from

1 0^{\circ} C

6 0^{\circ} C

is ______ s.
(Assume that the specific heat capacity of water remains constant over the temperature range of the water).

Answer: 300

Solution

The water needs

Q = m c Δ T = 2 \times 4200 \times (60 - 10) = 420000 J

to warm through

5 0^{\circ} C

. The heater draws

2000 W

but delivers only

70%

of it usefully, an effective rate of

0.70 \times 2000 = 1400 W

. The time to supply the required heat is

t = \frac{Q}{P _{eff}} = \frac{420000}{1400}

, which is

300 s

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer

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