Before going through the following articles, you should learn about the properties of gas, Boyle’s law and Charles’ law . You may find these on the following links :

**Introduction : **

We have discussed the relationship between the pressure and volume and relationship between the volume and temperature in Boyle’s law and Charles’ law respectively. Through these laws, we have a conclusion that the pressure varies inversely with the volume of the fixed mass of the gas at constant temperature and the volume of the fixed mass of the gas varies directly with the Kelvin temperature of the gas at constant pressure. Now let’s see what will be the relationship between the pressure and temperature of the gas at constant volume. This relationship is explained by the Gay Lussac’s Law.

## Statement of Gay Lussac’s Law of Pressure

For a given mass of a gas at constant volume, the pressure is increased or decreased by 1 / 273 parts of its initial pressure at 0 0 C on increasing for every 1-degree rise or fall in temperature.

**Mathematical form of Gay Lussac’s Law**

Let us assume that the volume of the fixed mass of a gas is kept constant.

P_{0} = initial pressure at 0^{0} C

For 1 ^{0} C rise in temperature, the increased pressure is given by

P_{1} = P_{0} + ( 1 / 273 ) P_{0}

For 2 ^{0} C rise in temperature, the increased volume is given by

P_{2} = P_{0} + ( 2 / 273 ) P_{0}

Similarly, for t ^{0} C rise in temperature, the increased volume is given by

P = P_{0} + ( t / 273 ) P_{0} = P_{0} ( 1 + t / 273 ) = P_{0} ( 273 + t ) / 273 = P_{0} T / 273

where T = ( 273 + t ) K =Tempearture in Kelvin scale

P / T = ( P_{0} / 273 )

( P_{0} / 273 ) = constant term

**P ∝ T**

P_{1} / T_{1} = P_{2} / T_{2}

**Graphical Representation of Gay Lussac’s Law**

**1 ) P -T graph :**

This graph explains that the kelvin temperature is directly proportional to the pressure of the gas when volume of a given mass of the gas is fixed.

**2 ) P – t graph :**

This graph is straight line having y – intercept. It represents the following equation.

P = P_{0} + ( P_{0} / 273 ) t

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