## SPECIFIC HEAT DEFINITION AND SAMPLE PROBLEM AND SOLUTION

The specific heat of a substance is the heat energy required to raise the temperature of unit mass of the substance by one degree. In terms of the quantities involved, the specific heat of a substance is the heat energy required to raise the temperature of l kg of the material by 1°C (or K, since they have the same interval on the temperature scale).

The units of specific heat are therefore J/kgK.

Different substances have different specific heats, for instance copper is 390 J/kgK and cast iron is 500 J/kgK. In practice this means that if you wish to increase the temperature of a lump of iron it would require more heat energy to do it than if it was a lump of copper of the same mass.

Alternatively, you could say the iron ‘soaks up’ more heat energy for a given rise in temperature. Remember that heat energy is measured in joules or kilojoules (1000 joules).

The only difference between the kelvin and the centigrade temperature scales is where they start from. Kelvin starts at –273 (absolute zero) and centigrade starts at 0. A degree change is the same for each.

The equation for calculating heat energy required to heat a solid is therefore the mass to be heated multiplied by the specific heat of the substance, c, available in tables, multiplied by the number of degrees rise in temperature, T.

Q = m.c. T
Putting in the units,
kJ = kg × kJ/ kg.K × K

Note that on the right-hand side, the kg and K terms cancel to leave kJ. It is useful to do a units check on all formulas you use.

SAMPLE PROBLEM WITH SOLUTION

1. The boiler in a canteen contains 6 kg of water at 20°C. How
much heat energy is required to raise the temperature of the
water to 100°C? Specific heat of water = 4190 J/kgK.
Q = m.c. T
Q = 6 × 4190 × (100 – 20)
Q = 2 011 200 J = 2011.2 kJ

2. How many kilograms of copper can be raised from 15°C to
60°C by the absorption of 80 kJ of heat energy? Specific heat
of copper = 390 kJ/kgK.
Q = m.c. T
80 000 = m × 390 × (60 – 15)
m =
80 000
390 × 45
= 4.56 kg