For this question, we must recognize that the system going to end up in equilibrium. That means that:

We are given the initial temperatures, masses, and specific heats of both the water and the ceramic. This will allow us to solve for the final temperature of the system; this value will be equal for both components. Notice that the specific heat given to us in the problem for the ceramic is in terms of kilograms, not grams. Convert to grams.

The equation for change in temperature is 

Plug in our given values.

Notice that the specific heats will cancel out.

Combine like terms.

The relationship between mass and temperature, when two masses are mixed together, is:

Using the given values for the mass and specific heat of each compound, we can solve for the final temperature.

We need to work to isolate the final temperature.

Distribute into the parenthesis using multiplication.

Combine like terms.

We will need to use Boyle's Law to solve:

Boyle's Law allows us to set up a relationship between the changes in pressure and volume under conditions with constant temperature. Since the equation is a proportion, we do not need to convert any units.

We can use the given values to solve for the new pressure.

For this problem, use Charles's Law:

In this formula, is the volume and  is the temperature. Charles's Law allows us to set up a proportion for changes in volume and temperature, as long as pressure remains constant. Since we are dealing with a proportion, the units for temperature are irrelevant and we do not need to convert to Kelvin.

Using the given values, we should be able to solve for the final temperature.

Cross multiply.

For this problem, use Boyle's Law: 

Boyle's Law allows us to set up a proportion between the pressure and volume at a constant temperature.

Using the values given, we can solve for the final pressure.

The volume of air in the balloon will increase when exposed to hotter temperatures, and decrease when exposed to colder temperatures. If we look at the ideal gas law, we can see that temperature and volume have a direct relationship. As one goes down, so does the other, assuming all other factors remain constant.

We can also look at Charles's law of volumes:

The balloon is sealed, so the amount of gas in the balloon will not change, and the elasticity of the balloon means that pressure will also remain constant. As temperature decreases, volume must also decrease. Suppose that the temperature is halved in our question. The result would be half the volume, according to Charles's law.

By this logic, we can conclude that the balloon will shrink when placed in the cold water.

Heat is a form of energy. Adding heat to a gaseous system will increase the energy of the molecules, causing them to move faster and collide more frequently. This increased velocity results in the expansion of the gas.

The formula for the net energy added to a system is;

The change in energy equals the heat energy minus the work done.

We don't know the work, but we can solve for it using the work equation:

We are given both the force and the distance, allowing us to calculate the work.

Now that we know both the work done and the heat added, we can solve for the final energy of the system.

The most likely explanation is that work is done by the system.

The formula for change in energy shows that the net change in energy is equal to the increase in heat energy minus the work done:

Since , there must have been work done by the system.