 # Relationship Between Temperature And Volume: Charles's Law

In 1787, the French scientist Jacques Charles discovered that volume of a gas varies when we change its temperature, keeping the pressure constant. Later, in 1802, Joseph Gay-Lussac modified the concept given by Charles and generalized it as Charles’s law. Gases obey Charles law at a very high temperature and low pressure.

Know more about Charles’s Law Formula

It can be stated as:

“The volume of a fixed mass of a gas decreases on cooling it and increases by increasing the temperature. For one degree rise in temperature, the volume of the gas increases by

$$\begin{array}{l}\frac{1}{273}\end{array}$$
of its original volume at 0˚C. Let volume of the gas at 0˚C and t˚C be Vo and Vt respectively”.

Then,

$$\begin{array}{l}V_t\end{array}$$
=
$$\begin{array}{l}V_o + \frac{t}{273.15} V_o\end{array}$$
……….. (i)

$$\begin{array}{l}V_t\end{array}$$
=
$$\begin{array}{l}V_o(1 + \frac{t}{273.15})\end{array}$$
……….. (ii)

$$\begin{array}{l}V_t\end{array}$$
=
$$\begin{array}{l}V_o (\frac{273.15 + t}{273.15}) \end{array}$$
…………  (iii)

We will now assign a new scale for temperature where the temperature in Celsius is given as t = T -273.15 and 0˚C can be given as To = 273.15. This new scale of temperature (T) is known as the Kelvin temperature scale or Absolute temperature scale. Degree sign is not written when a temperature is written in Kelvin scale. It is also known as the thermodynamic scale of temperature and it is commonly used in all scientific purposes. Thus, when we need to write temperature in Kelvin scale we add 273 to the temperature in Celsius.

Let us assume T = 273.15 + t

To = 273.15

Then equation (iii) can be written as

$$\begin{array}{l}V_t\end{array}$$
=
$$\begin{array}{l}V_o(\frac{T_t}{T_o})\end{array}$$

Or,

$$\begin{array}{l}(\frac{V_t}{V_o})\end{array}$$
=
$$\begin{array}{l}(\frac{T_t}{T_o})\end{array}$$

In general, we can write it as

$$\begin{array}{l}(\frac{V_2}{V_1})\end{array}$$
=
$$\begin{array}{l}(\frac{T_2}{T_1})\end{array}$$

Or,

$$\begin{array}{l}(\frac{V_1}{T_1})\end{array}$$
=
$$\begin{array}{l}(\frac{V_2}{T_2})\end{array}$$

• $$\begin{array}{l} \Rightarrow \frac{V}{T}\end{array}$$
=
$$\begin{array}{l} constant\end{array}$$
=
$$\begin{array}{l}k_2\end{array}$$
.

Hence,

$$\begin{array}{l}V\end{array}$$
=
$$\begin{array}{l} k_{2} T\end{array}$$
..

The value of k2 depends on the pressure of the gas, its amount and also on the unit of volume V.

Know more about Charles’s Law Calculator

Graphical representation:

At a fixed pressure, when the volume is varied, the volume-temperature relationship traces a straight line on the graph and on moving towards zero volume all lines intersect at a point on the temperature axis which is -273.15˚C. Each line in the graph of volume Vs temperature is known as isobar (Since pressure is constant). The least hypothetical temperature of -273˚C at which a gas will have zero volume is called as absolute zero. 