Question

What happens to the volume of gas as the temperature of a gas increases at a constant pressure?

Answer 1

Hint :Whenever we are solving a problem for the change in properties of gases, the first thing that comes to mind is the Ideal Gas equation. The ideal gas equation relates the pressure, volume, temperature, and moles of gas. As per the given conditions, we can remove the constant terms and find a proportionality relation between the required properties.

Complete Step By Step Answer:
Here, we are given that the pressure of the gas in a container is maintained at a constant value.
Let us first understand theoretically what might be the change in the volume of the gas when the temperature is increased.
Consider a piston-cylinder arrangement in which the piston is tightly attached to the walls of the cylinder and it moves without friction.
Now, as the temperature of the gas is to be increased, we assume that the cylinder is heated with a heating equipment.
Now, as the temperature of the gas increases, the particles of the gas start moving rapidly and thus the kinetic energy of the gas increases.
As the speed of the particles of the gas increases, the collisions of the particles with the walls of the cylinder and the piston increases.
As the collisions with the piston increases, the particles apply more pressure on the piston, which results in the increase of pressure.
However, here we are required to maintain constant pressure. Hence, the piston will move outwards in order to decrease the pressure.
As a result the pressure in the container remains constant, but due to the expansion the volume of the gas increases.
Hence, theoretically we can say that if the temperature is increased at constant pressure, the volume of the gas increases.
Let us prove this condition mathematically with the help of Ideal Gas equation given as,
 $ PV=nRT $
Here, the pressure is required to be constant and as the vessel is closed, the amount of gas inside the vessel remains constant. Rearranging the above equation,
 $ V=\dfrac{nR}{P}T $
All the values in the fraction are constant for the given case and hence, can be written as a single constant.
 $ \therefore V=kT $
Removing the constant, we get the proportionality relation as,
 $ \therefore V\propto T $
Hence, mathematically we can say that volume is proportional to temperature and if the temperature is increased at constant pressure, the volume of the gas increases.

Note :
The Ideal Gas equation used here, as explained is the combination of the Boyle’s Law, Charles’s Law, Gay-Lussac’s Law and Avogadro’s Law. However, these laws hold true only for the ideal gases, but we know that ideal gases are hypothetical and the properties of the real gases might not follow the proportionalities in these laws. Hence, whenever a change in property of gas is to be measured, we will assume the gas to be ideal to use the Ideal Gas Equation, unless specified otherwise.