Question

An electric heater rated as 2kW is used to heat 200kg of water from ${{10}^{^{\circ }}}C$ and ${{70}^{\circ }}C$. Assuming no heat losses , the time taken is:
$\begin{aligned} & \left( A \right)25.2s \\\ & \left( B \right)6\times {{10}^{3}}s \\\ & \left( C \right)25.2\times {{10}^{3}}s \\\ & \left( D \right)25.2\times {{10}^{6}}s \\\ \end{aligned}$

Answer 1

Electrical energy is a form of energy. By law of conservation of energy can neither be created nor destroyed. That is, they can be converted from one form of energy to another form of energy. Here the electrical heater converts electrical energy into heat energy. First calculate the temperature difference. From that find the rise in temperature and then calculate the energy required to increase the temperature of water by that change in temperature. Then use the concept that the energy required to heat the water is the same as the energy given by water in time t. Thus by equating those two equations and rearranging we will get the time taken.

Complete step by step answer:
Power of water $=2kW=2000W$
Mass of water=200kg
Difference in temperature,$\vartriangle T={{T}_{2}}-{{T}_{1}}$
Given that,
$\begin{aligned} & {{T}_{2}}={{70}^{\circ }}C \\\ & {{T}_{1}}={{10}^{\circ }}C \\\ \end{aligned}$
Substituting the values in the equation we get,
$\vartriangle T=70-10={{60}^{\circ }}C$
Energy required to heat the water=Energy given by water in time, $Q=pt$
Energy required to increase temperature of water by ${{60}^{\circ }}C$ is given by,
$Q=ms\vartriangle T$ …………….(1)
s is the specific heat.
$\therefore s=4200J/k{{g}^{\circ }}C$
Then,
$Q=pt$ ………..(2)
Hence equating (1) and (2) we get,
$pt=ms\vartriangle T$
Then substitute the given values and then rearranging we will get,
$2000\times t=200\times 4200\times 60$
$\Rightarrow t=\dfrac{200\times 4200\times 60}{2000}$
$\therefore t=25.2\times {{10}^{3}}\sec$

So, the correct answer is “Option C”.

Note: Electrical energy is a form of energy. By law of conservation of energy can neither be created nor destroyed. That is, they can be converted from one form of energy to another form of energy. Here the electrical heater converts electrical energy into heat energy. Thus power can also be defined as the work done per unit time. Then work done becomes the product of power and time. Here work done is in the form of heat energy. The Si unit of power is watt.