# Heat capacity & Specific heat capacity – explanation & measurement

In this post, we will first go for the definitions, formulas, units, and explanations of Specific Heat Capacity & Heat Capacity. Then we will see how to measure Specific heat capacity.

- Definition & formula of Heat Capacity or thermal capacity
- Definition & formula of Specific heat capacity
- specific heat capacity – Examples & values
- Explanation of different Heat capacity & Specific heat capacity of different materials
- Methods of measuring Specific heat capacity
- Calculation of energy using the formulas

## Definition & formula of Heat Capacity or thermal capacity

We define the thermal capacity C of an object as the energy required to raise its temperature by 1 K. Different objects (even different samples of the same substance) will have different values of heat capacity.

The formula of Heat Capacity or thermal capacity: **C = Q/ΔT**

SI Unit of Heat Capacity or thermal capacity: J K^{–1} or J °C^{–1}

## Definition & formula of Specific heat capacity

Specific heat capacity is the energy required to raise a unit mass of a substance by 1 K. ‘Specific’ here just means ‘per unit mass’.

The formula of Specific Heat Capacity: **c = Q/(mΔT)**

SI Unit of Specific Heat Capacity: J kg^{-1} K^{–1} or J kg^{-1} °C^{–1}

## specific heat capacity – Examples & values

Water has a specific heat capacity of 4200 J/(kg °C). Aluminium has a specific heat capacity of only 900 J/(kg °C).

This means, 4200 joules of energy are needed to raise the temperature of 1 kg of water by 1 °C. Similarly, 900 joules of energy are needed to raise the temperature of 1 kg of Aluminium by 1 °C.

Here is an infographic showing the specific heat capacity of different materials.

## Explanation of different Heat capacity & Specific heat capacity of different materials

In theory, if an object could be heated up with no energy loss, then the increase in temperature ΔT depends on three things:

• the energy that is given to the object Q,

• the mass, m, and,

• the substance from which the object is made.

Two different blocks with the same mass and same energy input will have a different temperature change.

In the following diagram, two different blocks of the same mass but made of different substances (say X and Y) are supplied with the same energy (say 1000 J). It is observed that the two blocks undergo different temperature changes. Substance X with fewer molecules will have a larger temperature change compared to substance Y with more molecules. This happens due to different heat capacities and specific heat capacities of X and Y substances.

## Methods of measuring Specific heat capacity

Let’s study a few methods of measuring Specific heat capacity. There are two basic ways to measure heat capacity.

### Measuring specific heat capacity using the Electrical method

The experiment would be set up as below:

the specific heat capacity c= (I V t) / m (T_{2}-T_{1}) = ( current x voltage x time ) / (mass x change in temperature)

Sources of experimental error

• the loss of thermal energy from the apparatus.

• container for the substance and the heater will also be warmed up.

• it will take some time for the energy to be shared uniformly through the substance.

### Measuring specific heat capacity using the Method of mixtures

The known specific heat capacity of one substance can be used to find the specific heat capacity of another substance.

Procedure:

• measure the masses of the liquids m_{A} and m_{B}.

• measure the two starting temperatures T_{A} and T_{B}.

• mix the two liquids together.

• record the maximum temperature of the mixture T_{max}.

If no energy is lost from the system then, *the energy lost by hot substance cooling down = energy gained by cold substance heating up*

**m**

_{A}c_{A}(T_{A }– T_{max}) = m_{B}c_{B}(Tmax – T_{B})**Now if we know the specific heat capacity of one substance in the equation, then the specific heat capacity of the other one in the equation can be calculated.**

Again, the main source of experimental error is the loss of thermal energy from the apparatus – particularly while the liquids are being transferred. The changes in temperature of the container also need to be taken into consideration for a more accurate result.

## Calculation of energy using the formulas

The energy that must be transferred to an object to increase its temperature can be calculated using this equation:

energy transferred = mass X specific heat capacity X temperature change

In symbols: energy transferred = m c (T2 – T1)

where m is the mass in kg, c is the specific heat capacity in J/(kg °C), and (T2-T1) represents the temperature change in °C (or in K).

The same equation can also be used to calculate the energy transferred when a hot object cools down.