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.

Calorimetry numerical Question: 6 [ref: Selina ICSE class 10]

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^oC to 38^oC. Assume that all the heat energy supplied by heater is given to the material.

Solution:

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

Mass of the material = 50 kg

Change in temperature △T = (38 – 18)⁰ C = 20⁰ C or 20 K

Power of heater P = 500 W

Heat energy required △Q = mc△T

△Q = 50 × 960 × 20

Say, Time taken by a heater to raise the temperature of material = t

Hence, Pt = △Q

t = △Q / P

t = (50 × 960 × 20) / 500

t = 1920 seconds

t = 32 minutes