Three ice cubes are used to chill a soda at
with mass
. The ice is at
and each ice cube has a mass of 6.0 g. Assume that the soda is kept in a foam container so that heat loss can be ignored and that the soda has the same specific heat as water. Find the final temperature when all ice has melted.
Strategy
The ice cubes are at the melting temperature of
Heat is transferred from the soda to the ice for melting. Melting yields water at
so more heat is transferred from the soda to this water until the water plus soda system reaches thermal equilibrium.
First we identify the known quantities. The mass of ice is
and the mass of soda is
Then we calculate the final temperature:
Significance
This example illustrates the large energies involved during a phase change. The mass of ice is about 7% of the mass of the soda but leads to a noticeable change in the temperature of the soda. Although we assumed that the ice was at the freezing temperature, this is unrealistic for ice straight out of a freezer: The typical temperature is
. However, this correction makes no significant change from the result we found. Can you explain why?
Like solid-liquid and and liquid-vapor transitions, direct solid-vapor transitions or sublimations involve heat. The energy transferred is given by the equation
, where
is the
heat of sublimation , analogous to
and
. The heat of sublimation at a given temperature is equal to the heat of fusion plus the heat of vaporization at that temperature.
We can now calculate any number of effects related to temperature and phase change. In each case, it is necessary to identify which temperature and phase changes are taking place. Keep in mind that heat transfer and work can cause both temperature and phase changes.
Problem-solving strategy: the effects of heat transfer
Examine the situation to determine that there is a change in the temperature or phase. Is there heat transfer into or out of the system? When it is not obvious whether a phase change occurs or not, you may wish to first solve the problem as if there were no phase changes, and examine the temperature change obtained. If it is sufficient to take you past a boiling or melting point, you should then go back and do the problem in steps—temperature change, phase change, subsequent temperature change, and so on.
Identify and list all objects that change temperature or phase.
Identify exactly what needs to be determined in the problem (identify the unknowns). A written list is useful.
Make a list of what is given or what can be inferred from the problem as stated (identify the knowns). If there is a temperature change, the transferred heat depends on the specific heat of the substance (
Heat Transfer, Specific Heat, and Calorimetry ), and if there is a phase change, the transferred heat depends on the latent heat of the substance (
[link] ).
Solve the appropriate equation for the quantity to be determined (the unknown).
Substitute the knowns along with their units into the appropriate equation and obtain numerical solutions complete with units. You may need to do this in steps if there is more than one state to the process, such as a temperature change followed by a phase change. However, in a calorimetry problem, each step corresponds to a term in the single equation
.
Check the answer to see if it is reasonable. Does it make sense? As an example, be certain that any temperature change does not also cause a phase change that you have not taken into account.
