# Latent Heats of Ices

When a material undergoes a phase transition from one state to another -- solid to liquid, liquid to gas, solid to gas -- it may release or absorb large amount of energy. Today, you will practice your skills in calorimetry by measuring

• the latent heat of fusion of water, as it changes from a solid to a liquid
• the latent heat of sublimation of carbon dioxide, as it changes from a solid to a gas

#### Latent heat of fusion of ice

Your lab manual describes the procedure by which you can measure the heat given off by a chunk of ice as it melts. Basically, you place an ice cube into an insulated cup of a known masss of water at a known temperature, let the cube melt completely, let the ice-water come to equilibrium with the original water, and then measure the temperature of the resulting mixture.

• following the procedure outlined in the lab manual, place an ice cube into the cup and start the experiment; don't measure the mass of the ice cube, you'll do that later
• wait for the temperature to reach an equilibrium,
• measure the mass of the mixture and figure out the mass of the ice cube
• calculate the latent heat of fusion of ice -- tell me your value as soon as you find it

• think about your experiment, and things that went wrong or led to large uncertainties. Then, modify your procedure to improve the final result, and try again.

How close is your value of the latent heat of fusion of ice to the value in your textbook? Did your modifications lead to a better result in the second trial?

Calculating the uncertainty in your value for latent heat of fusion is tough: there are several steps in the calculation, some of them additive and some multiplicative. You need to use different rules for combining uncertainties in the two different kinds of steps. You can do it, but it will take ten or fifteen minutes. Ask me for help if you don't know what to do.

Once you have a value for the uncertainty, you can check to see if your latent heat of fusion agrees with the textbook's value within the uncertainty.

#### Latent heat of sublimation of carbon dioxide

As a challenge, try a very similar experiment using a piece of solid carbon dioxide instead of ice. Solid CO2 will not melt into a liquid; instead, it will sublimate into a gas. Can you use the same apparatus to measure this procedure? Let's find out.

Follow the same procedure as you did for ordinary ice. Watch carefully for signs that gas is escaping from your calorimeter. Is there anything you can do to stop it from doing so?

• this time, determine the mass of the piece of CO2 before you place it into your calorimeter. Be quick -- it will be shrinking while you do it!
• start the experiment, just as you did for ice.
• once the mixture has settled to a final temperature, measure the mass of the mixture -- how much of the CO2 is still inside the container? What fraction of the CO2 escaped?
• calculate the latent heat of fusion of CO2

You may use this value for the latent heat of sublimation of C02:

```           246.3  BTU/lb
```
One BTU is the amount of energy required to raise the temperature of one pound of water by one degree Fahrenheit. Convert this value to Joules per kilogram before you compare it to the value you determined experimentally.

How close is your value of the latent heat of sublimation of CO2 to the value above?

You should hand in all your work before you leave the lab room. In addition to the items specified above, it should include

• Neat tables of all your measurements, including headings and all appropriate units and uncertainties
• All calculations
• A table which lists
• Each type of measurement you make this week
• The tool you used to make it
• The percentage uncertainty in your measurements using this tool
• The single largest source of error you can find in each experiment, and your recommendation for reducing it