Latent Heat of Fusion of Ice and Latent Heat of Vaporization of Water

 

Purpose

To investigate thermal energy conservation during a phase change, i. e., test the hypothesis that energy is conserved.

Preliminary Questions

1. We say ice melts and water freezes both at 0ūc at room pressure. Does this mean it is possible to have ice and water pressent at 0ūc?

2. We say water boils and steam condenses both at 100ūc at room pressure. Does this mean it is possible to have ice and water pressent at 100ūc?

3. You have ice in a glass of water. If the ice is melting, what must be true about the temperature of the ice at the surface and the temperature of the water at the ice surface (explain)?

4. Assuming there is a change occuring when ice melts, where does the energy for the change come from and is it being added or removed from the ice? If the energy flow stopped, would the melting stop and what would be the temperature if ice and water were present?

5. Assuming there is a change occuring when steam condenses, where does the energy for the change come from and is it being added or removed from the steam? If the energy flow stopped, would the condensing stop and what would be the temperature if steam and water were present?

6. Is water evaporating a change process? If not, why, if so, explain what the change is.

7. Compare the amount of energy required to melt 1g of ice at 0ūc to 5 g of ice at 0ūc. Compare the amount of energy required to boil 1g of water at 100ūc to 5 g of water at 100ūc.

8. Compare the amount of energy required to freeze 1g of water at 0ūc to 5 g of water at 0ūc. Compare the amount of energy required to condense 1g of steam at 100ūc to 5 g of steam at 100ūc. Is the energy flow in the same direction as in question 7?

9. If you took the amount of energy changes found in questions 7 and 8 and divided each energy by its associated mass, how would the values compare for steam - water and ice water separately?

10. In general, for the same material, explain why you would or would not expect the latent heat to be constant.

Apparatus

Double-walled calorimeter, ice which is melting, steam, water, thermometer, steam generator, paper towels, and balance.

 

Procedure (Note there is more detail because of time constraints on this lab.)

Caution, you will be working with steam this lab.

Define "phase of a substance" as the form it in which it appears to exist. For example, ice, water and steam are three phases of the substance called water. A phase change occurs when a substance goes from one phase to another.

Assume you can identify and quantify all the objects which gain and loose thermal energy (temperature related energy, colloquially called heat). If energy is conserved, then added the total energy gained by objects must equal the total energy lost by the other objects. (Can you explain why?)

E gained object 1, phase 1 + E gained object 1, phase change 1 + E gained object 1, phase 2 + E gained object 2, phase 1 +…
= E lost object 1, phase 1 + E lost object 1, phase change 1 + E lost object 1, phase 2 + E lost object 2, phase 1 +…

Assume the energy gained or lost during a temperature change while in the same phase is quantified by the specific heat (see the Calorimetry - specific heat laboratory exercise). The specific heat equation can be rearranged to

Echange = m c (T final -T initial)

or

E gained = m c (T final -T initial) and E lost = m c |T final -T initial| = m c (T initial -T final) .

Further, assume the

Assume the energy gained or lost during a phase change is quantified by the latent heat . The latent heat equation can be rearranged to

Echange = (+ if added, - if removed) m l

or

E gained = + m l and E lost = - m l.

 

These relations can be substituted into the energy conservation equation above.

Use the above relations to measure the unknown latent heat of ice - water and water - steam transitions.

(Note, the specific heat for water is defined as 1 = 4.186 at room temperatures and pressure.

The accepted value of the latent heat of fusion of water at room pressure is 80. = 335 .

The accepted value of the latent heat of vaporization of water at room pressure is 540. = 2260. .)

Hypothesize how your latent heat value for a should compare to the measured values others get for the same material.

 

A) Fusion of Ice

Ice water mixture

Find the mass of the calorimeter cup (mcup).

Fill the inner cup about half full with warm water (about 10 °C above room temperature if possible). (You may take water from a steam generator to get the higher temperature or try the hot water faucet.)

Find the mass of the water in the cup (mw).

Wait about 5 minutes and record the starting temperature of the water (Twi).

Take melting ice, dry it using a paper towel, quickly add the dried ice to the calorimeter cup . Add enough ice so that the cup is about 2/3 filled with ice and water.

Stir steadily, but not vigorously and monitor the temperature until a minimum is reached (Tf). (All the ice should be melted at this point, if not repeat adding less ice.)

Find the mass of ice turned to water that was added to the cup (mi).

Calculate the energy required to melt each gram of ice using energy conservation.

9. Repeat the experiment as instructed in class.

 

Analysis

Apply your energy conservation assumptions and determine the latent heat of fusion of ice at rooom pressure. Compare results.

B) Vaporization of Water

Steam Water mixture

Start with the steam generator about two-thirds full of water and begin heating the boiler with the lid on the top. A water trap may be used in the steam line (which should be as short as practically possible) to prevent hot water condensed in the tube from entering the calorimeter. (It is important that the hot water condensed in the tube be prevented from entering the calorimeter as much as possible (why?). If you don't have a trap, use a low spot in the hose. To get the water back into the steam generator, lift the hose up to let the water run back into the steam generator.)

Find the mass of the calorimeter cup (mcup).

Fill the inner calorimeter cup about two-thirds full of cool water at about 15 °C below room temperature. (Either the cool water from the heat-of-fusion experiment or fresh tap water may be used with some ice added to obtain the desired temperature. Make sure that all the ice has melted, however.)

Find the mass of the water in the cup (mw).

Gently stir the water and record the starting temperature of the water (Twi).

With the water in the steam generator boiling gently and steam flowing freely from the steam tube (as evidenced by water vapor coming from the tube, recall that steam is invisible), place the open end of the hose with escaping steam into the calorimeter water and stir. When the temperature of the water is about 15°C above room temperature, carefully remove the steam line from the calorimeter.

Stir gently, and record the final temperature (Tf).

Find the mass of steam turned to water that was added to the cup (ms).

Calculate the energy required to condense each gram of steam using energy conservation.

Repeat the experiment as instructed in class.

Analysis

Apply your energy conservation assumptions and determine the latent heat of vaporization of steam at rooom pressure. Compare results.

Questions:

 

1. What would be the final temperature if all the ice in the heat of fusion lab did not melt? Energy conservation could still be applied, but you need additional information. What else would you need?

2. Would it take more energy to melt 15 grams of ice, keeping the temperature of the resulting water at 0ūc, or more energy to take 15 grams of water from room temperature (20ūc) to 100ūc?

3. How much energy would be released by the steam if 2 grams of steam is condensed to water, staying at 100ūc?

How much energy would be released by 2 grams of water going from 100ūc to 37ūc (body temperature)?

How much energy would be released by 2 grams of steam at 100ūc going to water at 37ūc?

4. How would you change the energy conservation equation to include the change in temperature of the cup holding the water for each experiment?

5. It is found that the temperature of a substance during a phase transition doesn't change, e.g., ice going to water stays at the same temperature for both the ice and the water. However, it is necessary to add (or remove) energy to cause the phase change. The latent heats measure the amount of energy per unit mass of substance. If the energy added does not cause a temperature change, where does it go or what does it do?

6. A lake is covered with a layer of ice. Above the lake the air temperature is -20ūc and it is in thermal equilibrium with the top layer of the ice. At the bottom of the ice layer, the ice and the water are in equilibrium.

What must the temperature of the bottom of the ice and the water be, assuming ambient conditions?

Even though there is equilibrium, there is also a temperature gradient (it changes with location in a specific way). This means energy is flowing from the high to the lower temperature. Where is this energy coming from?

7. An igloo is made from ice. It shields the internal contents from the cold outside. With a person and / or a fire inside, it can be quite warm. If the internal surface of the igloo is melting, what is the minimum temperature inside the igloo at the ice surface?

8. Would hot water going into the cup (condensed steam) make the calculated Latent heat of vaporization too high or too low?

9. A person sweating and a dog panting have the same purpose to cool the body. In the process water undergoes a phase change from liquid to gas. Where does the energy come from for this transition? How does the process cool the body?

10. You can plot temperature versus energy added as a way to study thermal energy transformations. Imagine starting with water 100 grams and room pressure. Assume the temperature for the water is uniform. A plot with the intial temperature at -20ūc and the final temperature at 120ūc is shown below. Label regions where there is ice, water, steam, and mixed phases (identifying which phases are present). Label key temperatures (places of transition in the plot). Given the cice = 0.504 = 2.11 and csteam = 0.447 = 1.873 , find the total energy transfered during the process presented in the plot.