We
are solving series of problems based on the concept expansion of gases. When
heat energy is given expansion of gas is much bigger in scale than that of
solids and liquids due to weak molecular force of attraction among the gas
molecules. Expansion of gases has to be studied taking the impact of pressure
on it also as it plays a significant role. We have different gas laws to study
their motion. A gas is said to be ideal when it satisfy all gas laws at all
temperatures and pressures. But practically no gas is ideal and the existing
gases are called real gases. They obey gas laws only at high temperatures and
low pressures.

**Problem**

Density
of a gas at known temperature and pressure is given to us as shown in the
diagram below. We need to find the density of the system at different pressure
and temperature.

**Solution**

We
can rewrite the ideal gas equation in terms of density. Here we write volume of
ideal gas as the ratio of mass and density and mass of the gas is constant. We
can solve the problem as shown in the diagram below.

**Problem**

It
is given in the problem that at two different temperatures gas occupies
different volumes and we need to find the volume expansion coefficient of the
gas and the problem is as shown in the diagram below.

**Solution**

We
know that at constant pressure, volume of the gas is directly proportional to
the initial volume and change in the temperatures. Basing on that we can define
coefficient of volume expansion of the gas as the ratio of change in the volume
of the gas with its original volume per unit change in the temperature. Basing
on that we can solve the problem as shown in the diagram below.

**Problem**

It
is given in the problem that in a constant volume gas thermometer, gas is under
different pressures at two different temperatures and we need to find the
pressure of a gas at a different temperature. Problem is as shown in the
diagram below.

**Solution**

We
know that gas expansion cannot be studied under three parameters
volume,temperature and pressure. Hence we keep one parameter constant and study
the other two. Here volume is kept constant and it is found that change in the
pressure is directly proportional to the initial pressure and change in the
temperature. Basing on that coefficient of pressure expansion of gases is
defined. Given data is substituted in the formula and is solved as shown in the
diagram below.

**Problem**

The
length of air column and mercury thread in a quill tube is given to us and it
is given in the problem that the open end is in the upward direction. When the
tube is tilted by a certain angle with the horizontal,we need to find the
length of the air column. Problem is as shown below.

**Solution**

We
know that as the temperature of the system is constant, we can apply Boyle’s
law to solve the problem. Here in the place of volume we can write the product
of area of cross section of the tube and length of the pipe. Area of cross
section is constant here and hence the law can be rewritten as the product of
length and pressure is constant for a given gas. Basing on that the problem is
solved as shown in the diagram below.

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