Calorimetry

The Principle of Calorimetry

When two bodies at different temperatures are placed in thermal contact, heat flows from the hotter body to the colder one. The process continues until both bodies reach a common temperature — thermal equilibrium. Calorimetry is the experimental science of measuring the amount of heat transferred during such a process.

The central idea is simple: in an isolated system (one that does not exchange heat with the surroundings), the total heat lost by the hotter bodies equals the total heat gained by the colder bodies. This is the principle of calorimetry, and it follows directly from the law of conservation of energy.

The Calorimeter

The device used to carry out these measurements is called a calorimeter. A typical calorimeter consists of a cylindrical copper vessel with a stirrer, placed inside an outer jacket that provides thermal insulation. The vessel is usually polished on the outside to minimise heat loss by radiation. A lid with holes for a thermometer and the stirrer completes the assembly.

The substance under study is placed inside the inner vessel, and the temperature change is recorded with a sensitive thermometer. The stirrer ensures uniform temperature throughout the mixture.

Specific Heat Capacity and Heat Capacity

Before we can write the heat balance equation, we need two quantities that describe how a substance responds to heat.

The specific heat capacity $s$ (or $c$) of a substance is the amount of heat required to raise the temperature of a unit mass of that substance by one degree Celsius (or one kelvin). Its SI unit is $\text{J kg}^{-1} \text{K}^{-1}$.

If a mass $m$ of a substance undergoes a temperature change $\Delta T$, the heat $Q$ transferred is:

The heat capacity $C$ of a body is the amount of heat required to raise its temperature by one degree Celsius. It is simply the product of the body's mass and its specific heat capacity:

Its SI unit is $\text{J K}^{-1}$.

The Water Equivalent of a Calorimeter

A calorimeter itself absorbs heat when its temperature rises. To account for this, we use the concept of water equivalent. The water equivalent $W$ of a calorimeter is the mass of water that would require the same amount of heat as the calorimeter to raise its temperature by the same amount.

If the calorimeter has mass $m_c$ and specific heat capacity $s_c$, then:

(Since the specific heat capacity of water is $1 \text{ cal g}^{-1} {}^{\circ}\text{C}^{-1}$ in CGS units, the numerical value of $W$ in grams equals the heat capacity of the calorimeter in $\text{cal} {}^{\circ}\text{C}^{-1}$.)

The Heat Balance Equation

Consider a calorimeter of water equivalent $W$ containing a mass $m_1$ of water at an initial temperature $T_1$. A solid body of mass $m_2$, specific heat capacity $s_2$, and initial temperature $T_2$ (higher than $T_1$) is dropped into the water. The system is stirred, and the final equilibrium temperature $T$ is recorded.

The heat lost by the solid body is:

The heat gained by the water and the calorimeter together is:

where $s_w$ is the specific heat capacity of water.

Applying the principle of calorimetry:

This equation can be solved for any one unknown quantity — typically the specific heat capacity $s_2$ of the solid.

Determining Specific Heat Capacity: A Worked Method

Suppose we want to find the specific heat capacity of an unknown solid. The procedure is:

1. Measure the mass $m_2$ of the solid. …