Find the time taken by a 500 W heater to raise the temperature of 50 kg of material of specific heat capacity 960 J kg^-1 K^-1, from 18°C to 38°C. Assume that all the heat energy supplied by heater is given to the material.

Given,

Power of heater (P) = 500 W

mass of material (m) = 50 kg

Specific heat capacity of material (c) = 960 J kg^-1 K^-1

Change in temperature △t = (38 – 18)°C = 20° C = 20 K

From relation,

$Q = m c △t$

Substituting the values in the formula above we get,

$Q = 50 \times 960 \times 20 \\[0.5em] \Rightarrow Q = 960,000$

Now,

$Q = \text {Power} \times \text{time}$

Substituting the values in the formula above we get

$960,000 = 500 \times \text{time} \\[0.5em] \Rightarrow \text{time} = \dfrac{960,000}{500} \\[0.5em] \Rightarrow \text{time} = 1920 \text{ s}= 32 \text{ min} \\[0.5em]$

Hence, time taken = 32 min