Specific Heat Capacity

Take two different bodies of different material. Let the bodies be of same mass and size. If we provide equal amount of heat to both of them for ten minutes, then the rise in temperature is found to be different in the bodies. It is because of the different heat capacities of the bodies.
If $Q$ is the amount of heat required to produce $Δθ$ rise in temperature in a body of mass $m$, then it is found that, \[Q ∝m\] \[Q ∝ Δθ\] Combining these equations, we get, \[Q ∝ m Δθ\] \[∴Q=mSΔθ\] The proportionality constant $S$ is known as the specific heat capacity of the body.

If $m=1$ and $Δθ=1$, then \[S=Q\]
Thus, specific heat capacity of a substance is the amount of heat required to raise the temperature of unit mass of the substance through one degree.

Its SI unit is $\text{Joule kg}^{-1}°\text{K}^{-1}$ and its SI unit is $\text{Calorie g}^{-1}°\text{C}^{-1}$. Specific heat capacity is different for different substances.

Some Substances with their Specific Heat Capacity

From above table, we can see that water has very high specific heat capacity. So, it can absorb a large amount of heat without much rise in its temperature. That’s why, water is used to cool the engines of vehicles.

​In a desert, day is very hot while night is very cold. It is because the specific heat capacity of sand is less. So, its temperature changes fast. During days, the sand gets heated fast resulting a very hot day and during nights, the sand gets cooled fast, which results in a very cold night.

Thermal Capacity

Thermal Capacity of a body is defined as the amount of heat required to raise the temperature of the body through one degree. It is also known as the heat capacity of the body.
Consider a body of mass $m$ and specific heat capacity $s$. Then the amount of heat $Q$ required to raise the temperature of the body by $Δθ$ is given by, \[Q=msΔθ\] \[\text{ If Δθ=1, } Q=ms\text{ __(1)}\] This amount of heat is known as the thermal capacity of the body. Its SI unit is $\text{Joule °K}^{-1}$.

Water Equivalent

​Water equivalent of a body is defined as the mass of water that can absorb or emit the same amount of heat as is done by the body for same rise or fall in temperature. It is denoted by $W$. Its S.I. unit is $\text{kilogram}$ and C.G.S. unit is $\text{gram}$.

Consider a body of mass $m$ and specific heat capacity $s$. Then the amount of heat required to raise the temperature of the body through $Δθ$ is given by, \[Q=msΔθ\text{ __(2)}\]

Let $W$ be the water equivalent of the body. From definition, $W$ $\text{gram}$ of water also requires the same amount of heat to raise the temperature through $Δθ$. \[Q=WΔθ\text{ __(3)}\]

From $(2)$ and $(3)$, \[WΔθ=msΔθ\] \[W=ms\text{ __(4)}\] Thus, water equivalent of a body is equal to the product of its mass and specific heat capacity.

From $(1)$ and $(4)$, \[\text{Thermal Capacity}=\text{Water Equivalent}\] Thus, water equivalent of a body is numerically equal to the thermal capacity of the body.

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