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Calorimetry - Lesson Summary

Let’s take two iron bodies, A and B, at two different temperatures and place them in a thermally insulated box and see that they are in contact with each other. We know that heat energy flows from hot body to cold body.
Since they are in thermally insulated box, no heat escapes to surroundings. Heat energy emitted by the hot body must completely be absorbed by the cold body. Even when more than two bodies are placed in a thermally insulated box, some bodies lose heat energy and some other bodies gain heat energy.
That means “when two or more bodies at different temperatures are brought into thermal contact, and if no heat is allowed to escape to the surroundings, then the total heat lost by hot bodies must be equal to the total heat gained by cold bodies”. This is called “principle of calorimetry” Calorimetry “is the science of measuring heat.
The amount of heat lost or gained by a body is given by the equation
ΔQ = msΔT
Where “m” is the mass of the body, “s” is the specific heat capacity of the body, and “ΔT” is the change in temperature of the body.
We use water in the calorimeter. So we need to take a solid that is denser than water and insoluble in water.
Weigh the materials using a physical balance in the activity. First, the calorimeter with stirrer is weighed and let its mass be “m 1”. Then find the mass of the solid, m 2.Enough water is poured into the calorimeter and then the mass of the “calorimeter, stirrer and water” is found to be “m 3”.
Then mass of the water = m 3 – m 1
Note the temperature of the water, and let it be “t 1”.
Now heat the solid in the steam chamber of Renault’s apparatus till the thermometer in the apparatus shows a steady reading for few minutes, and let the temperature of the solid be “t 2”. The wooden partition ( Not shown in the adjacent figure) separating the steam chamber and the calorimeter provides thermal insulation to the calorimeter from the chamber so that there is no transfer of heat from the chamber to the calorimeter.

Now bring the calorimeter below the  slider at the base of the steam chamber, slide open the base of the chamber and drop the solid into the water in the calorimeter and stir the mixture for some time and then note down the equilibrium temperature “t 3
Let the specific heat capacity of the “copper” (for the calorimeter), “solid material”, and “water” be “s 1, s 2, and s 3 “respectively.
Here, heat is lost by the hot “solid material” and gained by the cold “calorimeter” and “water”.
Heat lost by the solid = m 2s 2 (t 2 – t 3)
Heat gained by the calorimeter = m 1s 1 (t 3 – t 1)
Heat gained by the water = (m 3 – m 1) s 3 (t 3 – t 1)
Applying the “principle of calorimetry” Heat lost by hot body = Heat gained by the cold body
m 2s 2 (t 2 – t 3) = m 1s 1 (t 3 – t 1) + (m 3 – m 1) s 3 (t 3 – t 1)
 s 2 = [m 1s 1 (t 3 – t 1)+(m 3 – m 1)s 3(t 3 – t 1)]/m 2(t 2 – t 3)


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