Question

How would you use the kinetic theory to explain why a helium filled balloon "shrinks" when it is taken from a warm room to the outside on a cold day?

Answer 1

We should have the basic idea about the kinetic energy concept of gaseous particles and we should have an idea about how the parameters like pressure, volume and temperature influence the kinetic energy of the gas and how they are interrelated.

Complete answer:
In the question, it is asked to comment on the observation that a balloon which is filled with helium gas shrinks when it is taken from a warm room and kept outside on a cold day. We have to explain the observation with the help of kinetic theory.
First we should have an idea about kinetic theory of gases.
We use the concept of kinetic theory to explain about the properties of gases. We know that the gaseous sample will be made up of a lot of particles which are in the microscopic range and we use these microscopic range measurements to establish the properties of the macroscopic substances.
We measure the parameters like pressure, volume, temperature etc. to explain about the properties of the gas.
The kinetic energy is formulated with few postulates. The idea we should have about kinetic energy to solve the given question is, the gaseous sample consists of several tint particles which are in continuous motion. And these tiny particles undergo elastic collisions between each other and also collide with the container. These collisions are measured as the pressure exerted by the container.
Another idea we should have is that as the temperature increases the average kinetic energy also increases, more particles will take place in the collision.
Now let us consider the given case with two equations for the kinetic theory of gases.
We know the equation that, $P=\dfrac{2NE}{3}V$
And the equation relating temperature is, $E=\dfrac{3kT}{2}$
E is the kinetic energy, P is pressure, V is volume, t is temperature and N is the number of molecules or particles in the gaseous sample.
So by comparing these two equations we could establish a relation between pressure, volume and temperature i.e., the pressure and volume is directly proportional to temperature of the system.
So as the temperature increases pressure and volume increases and hence the kinetic energy increases. But when the temperature decreases the volume and pressure decreases and the kinetic energy also decreases.
So when the balloon is kept at a region with lower temperature, the volume and pressure of the gas decreases and the balloon shrinks.

Note:
To solve such problems we should either know how the parameters are related or we should derive an equation or reaction which helps us to predict what will be the change observed by the macroscopic parameters when one among them changes, whether they are inversely proportional or directly proportional to each other. The gaseous molecules will not have any electrostatic force of attraction, they are only involved in collisions.