# Gas equation

From these two laws, we understand that the pressure, volume and absolute termperature of a gas are interrelated, and a change in any one produces a chage in the other two. Consider a given mass of a gas. Let its initial volume, pressure and absolute temperature be V1, P2 and T1, respectively. Now, change the pressure of the gas from P1 to P2 by keeping its temperature constant at T1 . As the pressure is changed from P1 to P2 the volume of the gas also changes, Let the new volume be V1 . By applying Boyle’s law,

PV1=P V                     (1.1)

⇒ V1 = P1 V1 /P2

Next, let the temperature be changed from T1 to T2 , by keeping the pressure constant at P2 Due to change in temperature, let its volume change from V1 to V2 Applying Charles’ law,

V1 / T1 = V2 / T2               (1.2)

⇒ V1 =( V2/ T2 )× T1

Equating (1.1) and (1.2), we get

P1 V1 / P1 = V2T1 / T2

P1 V1 / T1 = P2 V2 / T2 Or PV/T

the above equation is called gas equation.

## Explanation for Pressure of a Gas

Consider a gas enclosed in a container. The gas consists of a large number of molecules, moving all posible directions. As they move, they collide with each other and with the walls of the container, exerting force on it. The force exerted per unit area of the walls of the container is the gas pressure. With increase in temperature, the velocity of gas molecules increares and they exert more force and pressure, Thus, the pressure increases with temperature. The presure exerted by gas molecules also depends on the number of collisions par unit area, more is the pressure. When the volume of the container  is reduced, the number of collisions par unit area, more is  the pressure. When the volume of the container is reduced, the number of collisions, and bence, the pressure increases. Similarly, on increasing the volume, the number of collisions per unit area decreases and so the pressure also decreases.

The energy possessed by gas molecules in a container depends on their number per unit volume, their mass  and velocity. The velocity of molecules of diferent gases at room temperature  is given in the table below.

## Velocity of gas molecules at 300k

 S. No. Gas Molecular weight 10-3Kg/mole Velocity (m s-1 ) 1. H2 2.82 1920 2. H2O (Vapour) 18.0 645 3. N2 28.0 517 4. O2 32.0 483 5. CO2 44.0 412 6. SO2 64.1 342