Heat Equation and Specific Heat Capacity

Heat equation:

Let us consider a body having mass 'm' is heated so that its temperature changes from t₁ to t₂. Therefore, change in temperature is t₂ - t₁. The amount of heat "Q" depends on two factors i.e. mass of the body and temperature differences

I.e. Q∝m ........(i)

Q∝( t₂ - t₁)

Q∝dt ............ (ii) Where dt is temperature difference

Combining equation (i) and (ii)

Q∝mdt

Q = smdt

Therefore, Q = msdt

Where, 's' is proportionality constant and is known as specific heat capacity.

Specific Heat capacity:

we have,

Q = msdt

or, s = \(\frac{Q}{mdt}\)

When,

m = 1 kg

dt = 1 degree Celsius

s = Q

Thus, Specific heat capacity is defined as the amount of heat required to change the temperature of 1 kg of substances through 1°C or 1k

Unit of specific heat capacity:

We have,

S =\(\frac{Q}{mdt}\)

SI unit of heat energy (Q) is joule

SI of unit of mass (m) is kilogram

SI unit of change in temperature (dt) is Kelvin

Therefore, S =\(\frac{J}{kgK}\)=Jkg^-1K^-1

Note: Different substances have different specific heat capacity. The substance that has more specific heat capacity changes its temperature slowly (when it is heated its temperature rise up slowly and when it is cooled its temperature fall down slowly). The substances that have less specific heat capacity changes its temperature fast (when it is heated its temperature rise up quickly)

Specific heat capacity of some materials:

Thermal capacity:

Thermal capacity is defined as the amount of heat required to change the temperature of thesubstance through 1 degree Celsius. It is denoted by "C".

Mathematically,

C = m s where,

C = thermal capacity

M = mass of substance

S = specific heat capacity.

Its SI unit is J/K or J/°C

Principal of calorimetry:

It states that "The amount of heat lost by the hotter body is equal to the amount of heat gained by the colder body, avoiding external loss of heat."

Let us consider two bodies A and B where masses are m₁ and m₂. Let, t₁ and t₂ be the initial temperature of A and B respectively. Let specific heat capacity of A and B be S₁ and S₂ respectively. If A is hotter body and B is the older body when they are kept in thermal contact, A will lose heat and B will gain heat until their temperature becomes equal "t".

Now,

Amount of heat gained by B (Q₂) = m₂S₂(t - t₂)

Amount of heat lost by A (Q₁) = m₁S₁(t₁-t)

According to principle of calorimetry amount of heat loosed by A is equal to amount of heat gained by B

Therefore, m₁ S₁(t₁-t) = m₂ S₂ (t-t₂)