We
are solving series of problems based on the concept expansion of gases. When
heat energy is given to the gas, they get the heat energy and it spreads the
gas molecules quire far away and they fail to come back to their original
position and it leads to expansion. Gas is not having linear and areal
expansion and there is no particular shape and size. While we are studying
expansion of solids and liquids, we have not worried about the impact of
pressure as its impact is negligible and hence we had not taken that into
consideration. But in the case of gases, impact of pressure is big and it can
not be ignored.

There are three parameters here with gases like pressure,volume
and temperature and we can not study all three simultaneously. Hence we keep
any one parameter constant and study the other two parameters. If pressure is
kept constant, volume varies proportionate with temperature. If volume is kept
constant, pressure of the gas is directly proportional to its absolute
temperature and basing on that we can define coefficients of expansions of the
gas. It is proved that both the coefficient of expansions are same and it is
the same who is kept constant and who is variable is not going to make any
difference.

**Problem**

What
shall be the percentage change in the pressure of the gas when percentage
change in the volume of the gas is five percent at constant temperature and the
problem is as shown in the diagram below.

**Solution**

As
temperature is constant for a given gas, we can apply Boyle’s law. According to
this rule, product of volume and pressure of a given mass of the gas is
constant at the constant temperature. By applying the data of the problem as
shown in the diagram below and solve it.

**Problem**

An
air bubble doubles its radius on reaching the top of a water lake at constant
temperature and we need to know the depth of the water. Problem is as shown in
the diagram below.

**Solution**

Here
also we are going to apply Boyle’s law. We shall assume that the temperature of
the system is constant in this case. When the bubble is at the bottom of the
lake there is pressure on it due to water as well as atmosphere. When the
bubble reaches the top there is no water on its top and hence there is pressure
only due to atmosphere. Hence pressure on the top is less and hence the volume
will be more. By applying Boyle's law, we can solve the problem as shown in the
diagram below.

**Problem**

For
an ideal gas volume and temperature at two different constant pressures as
shown in the diagram below. We need to find the relation between two pressures.

**Solution**

At
constant pressure we can get the relation between volume and pressure basing on
the Charles law. The problem can be solved as shown in the diagram below.

**Problem**

Two
identical containers are connected by a capillary tube contain air at NTP
conditions. If one of the container is immersed in hot boiling water, what is
the new pressure. Problem is as shown in the diagram below.

**Solution**

As
the volume of the system is constant, we need to apply the relation that the
pressure is directly proportional to the absolute temperature. Initially the
two have different pressures. Temperature of one system is changed in the
problem and they together get a common pressure. Problem is solved as shown in
the diagram below.

**Problem**

Two
spheres of different volumes are connected with a capillary tube of negligible
volume as shown in the problem below. They contain ideal gas at given
temperature and pressure conditions. Keeping temperature of one constant and if
the temperature of the second is increased, we need to find the final pressure.

**Solution**

As
the number of moles of the gas is constant in the given case, we can apply
ideal gas condition to solve the problem. When temperature of one system is
changed , the total pressure of the system gets effected and we need to apply
ideal gas condition as shown in the diagram below to solve the problem.

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