Question

A 4 kw, 20 litre water heater is switched on for 10 minutes. The heat capacity cp for water is 4 kj/kg k. Assuming all the electrical energy has gone into heating the water, what is the increase of the water temperature?

Answer 1

Given:

A 4 kw, 20 litre water heater is switched on for 10 minutes. The heat capacity cp for water is 4 kj/kg k.

To find:

Increase in water temperature.

Calculation:

The total electrical energy be E :

$\therefore \: E = power \times time$

$= > \: E = 4000\times (10\times 60)$

$= > \: E = 4000\times 600$

$= > \: E = 24\times{10}^{5} \: joule$

Now , let change in temperature of water be denoted as $\Delta\theta$:

$\therefore \: E = m \times c \times \Delta\theta$

$= > \: 2400000= 20 \times 4000 \times \Delta\theta$

$= > \: 2400000= 80000 \times \Delta\theta$

$= > \: \Delta\theta =30 \: kelvin$

So, final answer is:

$\boxed{ \bold{\: \Delta\theta = 30 \: kelvin}}$