Explain heat capacity of substance and write its equation and unit.

Explanation

In the first step, heat a given quantity of water to raise its temperature by, say `20^(@)C` and note the time taken.
Again take the same amount of water and raise its temperature by `40^(@)C` using the same source of heat. Note the time taken by using a stopwatch.
You will find it taken about twice the time and therefore, double the quantity of heat required raising twice the temperature of same amount of water.
In the second step, now suppose you take double the amount of water and heat it, using the same heating arrangement, to raise the temperature by `20^(@)C`, you will find the time taken is again twice that required in the first step.
In the third step, in place of water, now heat the same quantity of some oil, say mustard oil, and raise the temperature again by `20^(@)C`. Now note the time by the same stopwatch. You will find the time taken will be shorter.
Therefore, the quantity of heat required for oil would be less than that required by the same amount of water for the same rise in temperature.
The above observation show that the quantity of heat required to warm a given substance depends on its mass, m, the change in temperature, `DeltaT` and the nature of substance.
The change in temperature of a substance, when a given quantity of heat is absorbed or rejected by it, is characterised by a quantity called the heat capacity of that substance.
Heat capacity S : Heat capacity is the ratio of heat given to substance `DeltaQ` and corresponding change in temperature `DeltaT`.
`:.S=(DeltaQ)/(DeltaT)`
Where `DeltaQ` is the amount of heat supplied to the substance to change its temperature from T to `T+DeltaT`.
Value of heat capacity depends on type of material and its mass.
Heat capacity of substance of same material but different mass can be different.
Unit of heat capacity is `"J K"^(-1)` or `"Cal K"^(-1)`.