Question

State Charles' Law Equation.

Answer 1

Charles' Law:

At constant pressure, the volume of a given mass of a gas increases or decreases by $\frac{1}{273}$of its volume at 0 degrees Celsius for every one-degree rise or fall in the temperature respectively.

Charles' law equation can be written as ${\mathrm{V}}_{\mathrm{t}}={\mathrm{V}}_0+\frac{{\mathrm{V}}_0}{273}\mathrm{t}$

• On rearranging, ${\mathrm{V}}_{\mathrm{t}}={\mathrm{V}}_0(1+\frac{\mathrm{t}}{273})$
• Further, ${\mathrm{V}}_{\mathrm{t}}={\mathrm{V}}_0\left(\frac{273+\mathrm{t}}{273}\right)$
• where t= temperature in Celsius
• The volume of gas at $0°\mathrm{C}$= ${\mathrm{V}}_0$ and volume of gas at $\mathrm{t}°\mathrm{C}$= ${\mathrm{V}}_{\mathrm{t}}$
• Also, $\mathrm{t}°\mathrm{C}+273=\mathrm{T}\left(\mathrm{K}\right)$
• Therefore, ${\mathrm{V}}_{\mathrm{t}}={\mathrm{V}}_0\left(\frac{\mathrm{T}}{273}\right)$ where T= Temperature in Kelvin
• On rearranging,${\mathrm{V}}_{\mathrm{t}}=\mathrm{T}\left(\frac{{\mathrm{V}}_0}{273}\right)$
• As $\frac{{\mathrm{V}}_0}{273}=\mathrm{constant}$

Hence, it can be concluded that the volume of a gas is directly related to the temperature of a gas at constant pressure. i.e.;$\mathrm{V}\propto \mathrm{T}$

• In simple words, as temperature increases, the kinetic energy of molecules increases.
• Due to this more force is exerted per unit area on the walls of the container. Therefore, pressure on the walls of the container will increase. But we have to keep pressure constant (condition of Charles law).
• The only way out to keep this increasing pressure constant is to increase the volume.
• Hence according to Charles' law volume increases as temperature increases at constant pressure.