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Specific Heat capacity formula

Specific Heat Capacity:

Specific heat of a substance is the amount of heat required as raise the temperature of 1 kg mass of that substance through 1 K.

Generally, when a body is heated, its temperature increases. Increase in the temperature of a body is found to be proportional to the amount of heat absorbed by it. It has also been observed that the quantity of heat ΔQ required to raise the temperature Δ T of a body is proportional to the mass of the body. Thus

         Δ Q ∝ m Δ T

or     Δ Q = c m Δ T ………….(1)

Here Δ Q is the amount of heat absorbed by the body and c is the constant of proportionality called the heat capacity of simple specific heat.



In SI units, mass m is measured in kilogram (kg), heat Δ Q is measured in Joule (J) and temperature increase Δ T is taken in kelvin (K). Hence, SI unit of specific heat bis Jkg-1 K-1. Specific heats of some common substances are given in table:

table of specific heat

Importance of Large Specific Heat Capacity of Water:

Specific heat of water is 4200 J Kg-1K-1 and that of dry soil is about 810 J Kg-1K-1. As a result the temperature of soil would increase five times more than the same mass of water by the same amount of heat. Thus, the temperature of land rises and falls more rapidly than that of the sea. Hence, the temperature variations from summer to winter are much smaller at places near the sea than land far away from the sea.

Water has a large specific heat capacity. For this reason, it is very useful in storing and carrying thermal energy due to its high specific heat capacity. The cooling system of automobiles uses water to carry away unwanted thermal energy. In an automobile, large amount of heat is produced by its engine due to which its temperature goes on increasing. The engine would cease unless it is not cooled down. Water circulating around the engine by arrows maintains its temperature. Water absorbs unwanted thermal energy of the engine and dissipates heat through its radiator.

In central heating systems such as hot water is used to carry thermal energy through pipes from boiler to radiators. These radiators are fixed inside the house at suitable places.

Heat Capacity:

Heat capacity of a body is the quantity of thermal energy absorbed by it for one kelvin (1 K) increase in its temperature.

Thus, if the temperature of a body increase through Δ T on adding  Q amount of heat, then its heat capacity will be ΔQ/ Δ T. Putting the value of Δ Q, we get:

Heat capacity = Δ Q/ Δ T = m c Δ T/ Δ T

heat capacity = m c ………..(3)

Equation (3) show that heat capacity of a body is equal to the product of its mass of the body and its specific heat capacity. For example, heat capacity of 5 kg of water is ( 5 kg × 4200 J kg -1 -1) 21000 JK -1. That is; 5 kg of water needs 21000 Joules of heat for every 1 K rise in its temperature. Thus, larger is the quantity of a substance, large will be its heat capacity.

Change of State:

Matter can be changed from one state to another. Foe such a change to occur, thermal energy is added to or removed from a substance.

change of state

Latent Heat of Fusion:

Heat energy required to change unit mass of a substance from solid to liquid state  at its melting point without change in its temperature is called its latent heat of fusion.

When a substance is changed from solid to liquid state by adding heat, the process is called melting or fusion. The temperature at which a solid starts melting is called its fusion point or melting point.When a process is reversed i.e., when a liquid is cooled, it changes into solid state. The temperature at which a substance changes from liquid to solid state is called its freezing point. Different substances have different melting points. However, the freezing point of a substance is the same as its melting point.

It is denoted by Hf.

        Hf = ΔQf/ m

or   Δ Qf  = m Hf … …. … … (4)

Ice changes at 0° C into water. Latent heat of fusion of ice  is 3.36 × 105 J kg -1. That is; 3.36 × 105 Joule heat is required to melt 1 kg of ice into water at 0°C.

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