# 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 Joule kg⁻¹°K⁻¹ and its SI unit is Calorie g⁻¹°C⁻¹ . Specific heat capacity is different for different substances.

## Some Substances with their Specific Heat Capacity

 S.N. Substance Specific Heat Capacity (Jkg-1◦C-1) 1. Lead 126 2. Gold 130 3. Mercury 140 4. Silver 234 5. Brass 380 6. Copper 380 7. Steel 447 8. Water Vapour 460 9. Iron 470 10. Glass 670 11. Sand 800 12. Aluminium 910 13. Air 993 14. Petrol 1670 15. Olive Oil 2000 16. Kerosene 2090 17. Ice 2100 18. Paraffin 2200 19. Ethanol 2590 20. Water 4200

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 Joule Kelvin⁻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 kilogram and C.G.S. unit is 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 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.