Question

An electric heater has resistance of $12\Omega$ and is operated from 220 volts power line. If no heat escapes from it time required to raise the temperature of 40 kg of water from ${15}^{o}C$ to ${80}^{o}C$ is (2700 + X) sec. Find the value of X.

Answer 1

Heat required $=(40\times {10}^3)\times 1\times (80-15)=26\times {10}^{5}cal$
Now, $H=\frac{V^{2}t}{R\times 4.2}cal$
$\therefore t=\frac{HR\times 4.2}{V^2}$
$\therefore t=\frac{26\times {10}^5\times 12\times 4.2}{220\times 220}=2708seconds.$

So $x=8$