Question

Explain the technique “method of mixtures’.

Answer 1

1. Method of mixtures is a technique used to determine specific heat capacity of a material using calorimeter.

2. In this technique a sample ‘A’ of the substance is heated to a high temperature which is accurately measured.

3. The sample ‘A’ is then placed quickly in the calorimeter containing water.

4. The contents are stirred constantly until the mixture attains a final common temperature.

5. The heat lost by the sample ‘A’ will be gained by the water and the calorimeter.

6. The specific heat of the sample ‘A’ of the substance can be calculated as follows:

• Let,

m₁ = mass of the sample ‘A’

m₂ = mass of the calorimeter and the stirrer

m₃ = mass of the water in calorimeter

s₁ = specific heat capacity of the substance of sample ‘A’

s₂ = specific heat capacity of the material of calorimeter (and stirrer)

s₃ = specific heat capacity of water

T₁ = initial temperature of the sample ’A’

T₂ = initial temperature of the calorimeter stirrer and water

T = final temperature of the combined system

• Using heat equation,

Heat lost by the sample ‘A’ = m₁s₁ (T₁ – T)

Heat gained by the calorimeter and the stirrer = m₂s₂ (T – T₂)

Heat gained by the water = m₃s₃ (T – T₂)

• c. Assuming no loss of heat to the surroundings, the heat lost by the sample goes into the calorimeter, stirrer and water,

∴ m₁s₁(T₁ – T) = m₂s₂(T – T₂) + m₃s₃(T – T₂) ………….. (1)

• Knowing the specific heat capacity of water and copper material of the calorimeter and the stirrer, specific heat capacity (si) of material of sample ‘A’ can be calculated.

e. Rearranging terms of equation (1),

7. One can find specific heat capacity of water or any liquid using the following expression, if the specific heat capacity of the material of calorimeter and sample is known