Specific Heat Formula

From the experiments, we know that the quantity of heat supplied Q is proportional to

mass of the substance (m)

increase in temperature t (t₂ - t₁)

Q = S m (t₂-t₁)------- (1)

S is the constant of proportionality. It is a characteristic feature of the substance and is known as its specific heat. From equation (1) we can write

Thus, specific heat of a substance may be defined as 'the quantity of heat required to increase the temperature of unit mass of the substance through 1^oC'.

In SI system unit mass = 1 kg

Specific heat is expressed in Joules/kg/K

From equation 1 we have

Q = m s (t₂-t₁)

If (t₂-t₁) = 1⁰C then Q is its thermal capacity.

Thus, thermal capacity (Q=ms)=mass x specific heat of the substance.

Thermal capacity is expressed in Joules/Kelvin.

Sub Topics

Specific heat of some of the substances
Importance of Specific Heat
Important points to note

Specific heat of some of the substances

Substance	specific heat in SI system –J/kg/K
Lead	128
Silver	134
Copper	386
Aluminium	900
Iron	448
Ethyl alcohol	2430
Water	4190
sea water	3900

Specific heat of copper is 386 J/kg/K means '1kg of copper requires 387 J of heat energy to increase its temperature by 1k'.

We may note that the specific heat of water is the highest. It requires nearly 4200 Joules of heat energy to increase the temperature of 1 Kg of water by 1K. Infact, water has one of the highest specific heats of all matter. Liquid ammonia with a specific heat of 5040 J/Kg/Kelvin is one of the few substances with a value higher than that of water.

Importance of Specific Heat

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The specific heat of a substance is an important physical property because it tells us the suitability of a given substance for a specific purpose. Aluminium vessels are used in cooking because aluminium is a light metal. Hence, for a given volume, its thermal capacity will be less than that of vessels made of steel of same volume.

The high specific heat of water explains why land close to a large pond of water is likely to have a milder climate than land without a pond close by. Because of high specific heat, water on the land gets heated slowly. Land near the pond also gets heated slowly. For the same amount of heat, dry land gets heated quickly to a much higher temperature. Soil is a poor conductor, prevents the heat from going deep into the ground. Hence, the heat causes a quick rise in temperature on dry land. For same reasons, land areas far from water-cool off much faster than land near large bodies of water.

Important points to note

specific heat at constant volume

specific heat at constant pressure.

When a gas absorbs heat at constant volume, all the heat energy supplied is used to rise its temperature.

When a gas absorbs heat at constant pressure, part of the energy supplied is used to do external work.

Therefore, specific heat at constant pressure of a gas is greater than specific heat at constant volume by an amount equal to the external work done during expansion.