Question

An electric immersion heater is switched on for 8 minutes. The heat supplied by it raises the temperature of 500g of water from ${{10}^{o}}C\text{ to 6}{{\text{0}}^{o}}C$. Calculate the power of the heater in watts.

Answer 1

We have been provided with an electric immersion heater which is on for8 min. considers to calculate power of heater, law of conservation of energy. Consider Since we know that energy supplied by a heater is a product of power and time. Consider whereas heat energy absorbed by water is given by expression of specific heat capacity. And according to the law of conservation of energy, energy supplied by a heater is equal to heat energy absorbed by water. Hence calculate power.

Formula used:
Energy supplied by water = $P\times t$
Where, P = power of heater, t = time.

Complete step by step answer:
An electric immersion heater is switched on for 8 min. Let, t be the time then,
Time (t) = 8min = 480s
Now the heat is supplied by water of 500g and it raises the temperature of water from${{10}^{o}}\text{C to 6}{{\text{0}}^{o}}C$. Now, we have to calculate the power of the heater in watts. Let, p is the power of heater then energy supplied by heater is given by,
$\begin{aligned} & E=P\times t \\\ & E=P\times 480s \\\ \end{aligned}$
Also, rise in temperature of water ${{\theta }_{R}}$ is given by,
$\begin{aligned} & {{\theta }_{R}}={{\left( 60-10 \right)}^{o}}C \\\ & {{\theta }_{R}}={{50}^{o}}C \\\ \end{aligned}$
Therefore, heat energy absorbed by water is given by,
$Q=mc{{\theta }_{R}}$
Where, c is called as specific heat of water and value of c is $4.2j{{g}^{-1}}{}^\circ {{C}^{-1}}$
Put value we get,
$\begin{aligned} & Q=500g\times 4.2\times 50 \\\ & =105000J \\\ \end{aligned}$
Therefore, according to law of conservation of energy, energy supplied by heater is equal to heat energy absorbed by water i.e.
$\begin{aligned} & P\times 480\sec =105000j \\\ & P=\dfrac{105000}{480}=219j{{s}^{-1}}\text{ or watt} \\\ \end{aligned}$

Hence, the power of the heater in watt is 219 watt.

Note: We know that specific heat can be called as specific heat capacity denoted by c. value of c for water is $4.2j{{g}^{-1}}{}^\circ {{C}^{-1}}$, it means that $4.2j{{g}^{-1}}{}^\circ {{C}^{-1}}$of energy must be added to 1g of water to raise its temperature by ${{1}^{o}}C$ the amount of heat required to change the temperature of a substance is directly proportional to the mass of the substance and change in temperature.