Chapter 5, Problem 15STP

To determine

To explain: The process by which the given object measures the specific heat of materials.

Explanation of Solution

Introduction:

Specific heat capacity of a substance is defined as the amount of heat required to increase the temperature of 1 kg of a substance by 1 ${}^{\text{o}}\text{C}$ .

The diagram is for calorimeter. It is used to measure the heat of chemical reactions or heat capacity of materials. It consists of thermometer which is attached to metal container with water suspended above chamber where combustion takes place.

The process is based on the conservation of energy. Here, heat is a form of energy which is transferred between sample (whose specific heat needs to be determined) and water (with known specific heat). The change in the temperature of the water is measured in the calorimeter. This change in temperature helps to calculate the heat change of the sample.

The mathematical relation is represented as follows:

  $Q_w =–Q_s$

Here, $Q_w$ is heat change in water and $Q_s$ is heat change in sample. The negative sign indicates heat gain is equal to heat loss.

If heat change in the sample, $Q_s$ is known, change in temperature, $\Delta T\text{ or}\left(T_2-T_1\right)$ is known and mass of sample, m is also known, the specific heat capacity of the substance or sample can be calculated using the following relation:

  $Q_s=mC\Delta T$

Or,

  $C=\frac{Q}{m\left(T_2-T_1\right)}$

Here, C is specific heat capacity of the sample.

Conclusion:

Thus, from the given object that is calorimeter, the specific heat capacity of any substance can be calculated using the following relation:

  $C=\frac{q}{m\left(T_2-T_1\right)}$

Here, $q$ is heat, m is mass, $T_2$ is final temperature and $T_1$ is initial temperature.