CALORIMETRY

When two bodies (one being solid and other liquid or both being liquid) at different temperatures are mixed, heat will be transferred from body at higher temperature to a body at lower temperature till both acquire same temperature. The body at higher temperature releases heat while body at lower temperature absorbs it, so that

Heat lost = Heat gained

i.e. principle of calorimeter represents the law of conservation of heat energy.

(1) Temperature of mixture (T) is always ≥ lower temperature (T_L) and ≤ higher temperature (T_H), i.e.

T_L ≤ T ≤ T_H

i.e., the temperature of mixture can never be lesser than lower temperatures (as a body cannot be cooled below the temperature of cooling body) and greater than higher temperature (as a body cannot be heated above the temperature of heating body). Furthermore usually rise in temperature of one body is not equal to the fall in temperature of the other body though heat gained by one body is equal to the heat lost by the other.

(2) When temperature of a body changes, the body releases heat if its temperature falls and absorbs heat when its temperature rises. The heat released or absorbed by a body of mass m is given by,

Q = mc DT

Where c is specific heat of the body and DT change in its temperature in ^oC or K.

(3) When state of a body changes, change of state takes place at constant temperature [m.pt. or b.pt.] and heat released or absorbed is given by,

Q = mL

Where L is latent heat. Heat is absorbed if solid converts into liquid (at m.pt.) or liquid converts into vapours (at b.pt.) and is released if liquid converts into solid or vapours converts into liquid.

(4) If two bodies A and B of masses m₁ and m₂, at temperatures T₁ and T₂ (T₁ > T₂) and having gram specific heat c₁ and c₂ when they are placed in contact.

Heat lost by A = Heat gained by B

Or 

m₁c₁ (T₁ - T) = m₂c₂ (T – T₂)

[Where T = Temperature of equilibrium]

T = (m₁c₁T₁ + m₂c₂T₂)/ (m₁c₁ + m₂c₂)

• If bodies are of same material c₁ = c₂ then T = (m₁T₁ + m₂T₂)/ (m₁ + m₂)
• If bodies are of same mass (m₁ = m₂) then T = (T₁c₁ + T₂c₂)/ c₁ + c₂
• If bodies are of same material and of equal masses (m₁ = m₂, c₁ = c₂) then T = (T₁ + T₂) / 2