Calculate the time required(in minutes) to heat 20 kg of water from 10°C to 35°C using an immersion

Question

Calculate the time required(in minutes) to heat 20 kg of water from 10°C to 35°C using an immersion heater rated 1000 W. Assume that 80% of the power input is used to heat the water. Specific heat capacity of water = 4200 J/kg-K.

Professor PC Thomas Classes · Answer

To calculate the time $t$ :
1. Energy Required $(Q): Q=m \cdot c \cdot \Delta T=20 	imes 4200 	imes 25=\mathbf{2}, \mathbf{1 0 0}, \mathbf{0 0 0 ~ J}$
2. Effective Power ( $P$ ): $P=1000 \mathrm{~W} 	imes 0.80=800 \mathrm{~W}$
3. Time $(t): t=\frac{Q}{P}=\frac{2,100,000}{800}=\mathbf{2 6 2 5}$ seconds
$\mathbf{4 3 . 7 5}$ minutes (or 43 min 45 sec ).