The formula for heat energy is:

We are given the initial and final temperatures, mass, and specific heat. Using these values, we can find the heat released. Note that the time is irrelevant to this calculation.

That means that the soup "lost"  of energy. This is the amount that it released into the room. The value is negative for the soup, the source of the heat, but positive for the room, which receives it.

The formula for heat energy is:

We are given the final temperature, mass, specific heat, and heat released. Using these values, we can find the initial temperature. Note that the time is irrelevant to this calculation. Since heat is released from the soup, the net change in the soup's energy is negative. Since the soup is cooling, we expect our answer to be greater than .

The formula for heat energy is:

We are given the initial temperature, mass, specific heat, and heat released. Using these values, we can find the final temperature. Note that the time is irrelevant to this calculation. Since heat is released from the soup, the net change in the soup's energy is negative. Since the soup is cooling, we expect our answer to be less than .

When an object changes phase, it requires energy called "latent heat." In this case, even though the temperature is remaining constant, the energy inside of the ice cube is decreasing as it expends energy to melt.

The equation for two items reaching a thermal equilibrium is given by describing a heat transfer. The heat removed from one object is equal to the heat added to the other.

We are given the specific heat values of each substance, as well as their masses. We also know the initial temperature of each substance. Use these terms in the equation to solve for the final temperature. Remember that the final temperature will be the same for each substance, since they will be in thermodynamic equilibrium.

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.