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 10°C to 60°C is _________ s. (Assume that the specific heat capacity of water remains constant over the temperature range of the water). Numerical answer type. Work it out, then open the answer.

Answer: 300. Useful power = 0.7 × 2000 = 1400 W Heat needed = 2 × 4200 × 50 = 4.2 × 10⁵ J t = (4.2 × 10⁵)/(1400) = 300 s

A water heater of power 2000 W is used to heat water. The specific… | JEE Main 2023 (31 Jan, Shift 2)

Q18JEE Main 2023 · 31 JAN · SHIFT 2Medium

Calorimetry, Latent Heat & Mechanical Equivalent of Heat

A water heater of power $2000\text{ W}$ is used to heat water. The specific heat capacity of water is $4200\text{ J kg}^{-1}\text{ K}^{-1}$ . The efficiency of heater is $70\%$ . Time required to heat $2\text{ kg}$ of water from $10^{\circ}\text{C}$ to $60^{\circ}\text{C}$ is _________ s.

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

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 300

Useful power $= 0.7 \times 2000 = 1400\text{ W}$
Heat needed $= 2 \times 4200 \times 50 = 4.2 \times 10^5\text{ J}$
$t = \dfrac{4.2 \times 10^5}{1400} = 300\text{ s}$

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