Question

A heater, rated $1000W$, is used to heat $1.5kg$ of water at $40°C$ to its boiling point. Calculate the time in which the water starts to boil. Specific heat capacity of water is $4200JK{g}^{-1}°C^{-1}$.

Answer 1

Step 1

Given:

1. Power of heater (P) $1000W$,
2. Mass of water(m) $1.5kg=1500g$
3. Change in temperature of water from $40°C$ to its boiling point

Find:

The time in which the water starts to boil

Step 2:

Let the time required is t

We know that the boiling point of the water is $100°C$

Change in temperature is ${\theta }_R=100°C-40°C=60°C$

The heat energy absorbed by water is given as $mc{\theta }_R=1500\times 4.2\times 60=378000$

Step 3:

By the law of the conservation of energy we have

$$\begin{gathered} P\times t=378000 \\ 1000\times t=378000 \\ t=378s \end{gathered}$$

Hence after $378seconds$ water will start boiling.