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

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

<p>The amount of heat energy required to raise the temperature of a substance can be calculated as:</p> <p>Q = m $\times$ c $\times$ ΔT</p> <p>where Q is the heat energy required, m is the mass of the substance, c is its specific heat capacity, and ΔT is the change in temperature.</p> <p>The time required to heat a substance can be calculated as :</p> <p>t = ${Q \over P}$</p> <p>where t is the time required, and P is the power of the heating device.</p> <p>The actual power output of the heating device can be calculated as:</p> <p>P_actual = P_input $\times$ efficiency</p> <p>where P_input is the input power to the device and efficiency is the fraction of input power that is actually converted to useful power output. </p> <p>Substituting the given values:</p> <p>Q = 2 kg $\times$ 4200 J/kg/K $\times$ (60 - 10) = 2 kg $\times$ 4200 J/kg/K $\times$ 50 K = 4200 $\times$ 50 $\times$ 2 J = 420,000 J</p> <p>P_input = 2000 W = 2000 J/s</p> <p>P_actual = 2000 $\times$ 0.7 = 1400 J/s</p> <p>t = ${Q \over {{P_{actual}}}}$ = ${{420,000} \over {1400}}$ J/s = 300 s</p> <p>So, the time required to heat 2 kg of water from 10°C to 60°C is approximately 300 s.</p>