Heat Capacity, C, is defined as how much heat must be added to a substance to raise its temperature by 1℃ or 1K. Heat capacity, in plain terms, is an index of an object's ability to resist being warmed by the addition of heat energy. By comparison, specific heat capacity, c, is how much heat must be added to 1 gram of a substance to raise its temperature by 1℃ or 1K. (Remeber from our previous lesson that the Kelvin scale is based on the Celsius scale, and so the increase of 1℃ is the same as an increase of 1K).
Notice that the only difference between heat capacity and specific heat capacity is that specific heat capacity is based on the mass of the substance. It shows the heat energy in joules required per unit of mass to raise the temperature. Specific heat capacity refers to specifically 1 gram of the substance and is measured in J/kgK.
Heat capacity is the ratio of the amount of energy transferred to a material and the change in temperature that is produced, and it is measured in J/K. Heat capacity is calculated like this:
C = Q / ΔT
Q = heat energy in joules and
ΔT = change in temperature
To calculate specific heat capacity, you simply divide the heat capacity by m, the mass of the substance:
c = (Q / ΔT)/m
c = C/m
Based on this, we can calculate the heat energy in a certain substance:
Eʜ = mc ΔT
or Q = mcΔT
Eʜ or Q = heat energy in joules
The two quantities, heat capacity, C and specific heat capacity, c are related by the following equation:
C = mc
Where m = mass of the substance.
a) How much energy is needed to heat up 1kg of water by 15°C?
Eʜ = mc ΔT
= 1 kg x 4200 J/kg°C x 15°C
= 63000 J
= 63 kJ
b) What will be the temperature change if you used 1125J of energy to heat a block of iron weighing 0.5kg?
Here, we simply rearrange the equation we used above to find ΔT:
ΔT = Eʜ/mc
= 1125 J/(0.5 kg x 450 Jkg°C⁻¹)