## Friday, January 6, 2017

### Expansion of Gases Problems with Solutions One

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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