Grade 11 - Physics - Kinetic Theory - Introduction - Basics Fundamentals

Laws of expansion
All gases expand on heating. The expansion of its container can be neglected as the expansion of gas is so large.
The gases can be compressed easily, even they expand in volume at a constant temperature, provided the pressure is allowed to fall.
The volume of gas depends on temperature and pressure as follows
1. Change in volume due to change in pressure when temperature remains constant. This is given by Boyle’s law.
2. Change in volume due to change in temperature when pressure remains constant. This is given by Charle’s Law.
3. Change in pressure due to change in temperature when volume remains constant. This is given by Pressure law.

Boyle’s Law

Boyle’s law states that for a fixed mass of a gas, the volume varies inversely with its pressure provided the temperature remains constant.
Thus,

Where p is the pressure and V is the volume.
Alternatively, if V1 is the volume at pressure P1 and V2 is the volume at pressure P2 then at constant temperature,
P1V1 = P2V2
From Boyle’s law it follows that if the volume of the gas reduced to one – half, its pressure will be doubled.
Analysis
The following points should be noted carefully :
Energy consideration
The product of pressure and volume has the dimensions of energy, thus the statement that pV = constant at a particular temperature implies that energy of a gas at a constant temperature has a constant value.
Ideal gas
No real gas obeys Boyle’s law fully, although it is followed approximately by all gases. A gas which obeys Boyle’s law fully is known as perfect gas or an ideal gas.
For an ideal gas a graph between (pV) and p is a straight line parallel to p –axis, but this is not so for a real gas.Fig. ------
Alternative form

The mass m of a gas is related to its density ? by the relation
The Boyle’s law equation, pV = constant can be written as

Further, since the mass m of the gas does not change, Boyle’s equation can be written in the following form:

An alternative statement of Boyle’s law is –
At constant temperature the density of a gas increases directly with its pressure.