# Lab 11: Latent Heat of Fusion

Adapted for online learning by Leo Silbert

# Materials

• Thermometer Online Simulation

http://physics.bu.edu/~duffy/HTML5/thermometer.html

http://physics.bu.edu/~duffy/HTML5/ice_and_water.html

Lab 11 Learning Objectives

After successful completion of this lab, students will be able to:

• Recognize the existence of different temperature scales;
• Practice unit conversions;
• Measure temperature changes of different substances;
• Predict the thermal properties of different substances.

# Introduction

Generally, when you add heat (as with a flame or electric heater) to a material, its temperature increases. If “Q” represents the heat flow into or out of a given mass “m” and “∆T” represents the change in temperature (remember, “change in” = final value – initial value), we define the specific heat capacity “c” by the relationship.

Equation 1

If the heat energy is measured in calories, the mass in grams and the temperature in degrees Celsius (°C), then the specific heat capacity specifies how many calories it takes to change the temperature of one gram of the material by one degree. The calorie is defined as the amount of heat energy required to raise the temperature of 1 gram of water by 1°C.  Hence, the specific heat capacity of water is 1.00 cal / (g . °C). Note: We use these units rather than SI units to give “c” a numerical value of “1” for water.

When a substance undergoes a phase change from solid to liquid (melting), energy is required to break the bonds holding the molecules “rigidly” in place. In this case, it is possible for heat energy to be added with no change of temperature. We define the latent heat of fusion Lf as follows.

Equation 2

The latent heat of fusion represents the energy required to melt one gram of a material when its temperature is already at the melting point.

Q1. Given the previous definitions, make the followingprediction. Rank in the order of how much energy is required from greatest energy to least energy. If you think that any take the same energy, circle their numbers in your ranking.

(1)  Raising the temperature of 1 gram of water 1°C.

(2)  Raising the temperature of 1 gram of water 2°C.

(3)  Raising the temperature of 2 grams of water 1°C.

(4)  Raising the temperature of 1 gram of water from 0°C to 100°C.

(5)  Changing 1 gram of ice at 0°C to 1 gram of water at 0°C (melting).

(6)  Changing 2 grams of ice at 0°C to 1 gram of water at 0°C with 1 gram of ice at 0°C floating in it.

RANKING:                     _____     _____     _____     _____     _____     _____

# Activity 1 Measuring Temperature

• A thermometer is a device to read off temperature. You can measure temperature in different units just like you can measure length in either feet or meters. A widely-used unit for temperature is the Celsius temperature scale, where water freezes at 0°C and boils at 100°C at sea level. The thermodynamic, or absolute, temperature scale is measured in Kelvin (K). This scale defines what we mean by “absolute zero”. Navigate your web browser to the Thermometer Online Simulation

This simulation shows you a thermometer with a variety of temperatures listed. If you have a thermometer around your house, like a fridge magnet thermometer, go look up (your kitchen) room temperature, otherwise, use a value of 20 °C. Now turn to the simulation and adjust the scale until the value matches room temperature and write these down for the different temperature scales listed:

Room Temperature:    __________ °C            __________ °F            __________ K

Real thermometers, however, do not respond instantly. For example, when taking your body temperature with a standard liquid-in-glass thermometer, you wait minutes for the thermometer reading to stabilize. Do this remind you of a recent lab?

We will explore temperature change and heat flow in Activity 2. For now, imagine you go to your medicine cabinet and dig out a liquid-in-glass thermometer. (If you have one, do this now.)

Q2. From a thermodynamic point of view, explain why do you think it takes a couple of minutes for the thermometer reading to stabilize?

Activity 2 Temperature Change and Heat Flow

You will start this activity with a prediction and then you will test it.

Suppose you have an insulated beaker of water at room temperature and a hot block of metal. Metals typically have a specific heat that is smaller than that for water. You heat up a block of iron to a temperature of 200°C and then place it in the water inside the beaker – this is known as a calorimeter. Room temperature is 20°C.

Q3.  Predict what you think the final temperature of the block will be. Will it be midway between the two temperatures? Or will it be closer to 200°C? Or closer to 20°C? Discuss your reasoning.

•

Your screen should look like this (a basic type of calorimeter):

Figure 1: Snapshot of the online simulation lab for Activity 2.

1. For the left beaker, click on “SOLIDS”, then choose Iron – Fe
2. Use the Mass slider to set the mass to 50g
3. Use the Temp slider to set the temperature to 200°C
4. Check the Show specific heat button
5. Make a note of your information:

Mass of iron: miron = _________g

Initial temperature of iron: Tiron = ________°C

Specific heat of Iron: ciron = ___________J/g.K

Click blue box “Next”

Now you want to fill the calorimeter with water.

1. Choose water.
2. Set the water mass to 50 g
3. Leave the temperature setting to 20.0 oC
4. Check the Show specific heat button
5. Make a note of your information:

Mass of water: mwater = _________g

Initial temperature of water: Twater = ________°C

Specific heat of water: cwater = ___________J/g.K

Q4. Use your information to convert the specific heats. The information for water is already given as a guide:

specific heat of water, cwater =   4.184    J/g.K    =    1.00    cal/g.°C

specific heat of iron, ciron = __________ J/g.K    =   _____cal/g.°C

Click blue box “Next”

On the right, check the Show graph view. You are now in a position to run your experiment.

When you do click Start, a graph will pop up showing you how the temperature of the water and the iron in the calorimeter evolves with time. The temperature dial will change accordingly until the water reaches a new state of thermodynamic equilibrium. This final temperature is the same for both the water and the iron block.

Record the final equilibrium temperature (with iron):     ________°C

Q5. Check if your results agree or disagree with your prediction (Q3). Now think about what happens as the hot iron block cooled down. What happened to the water? Explain this in terms of heat flow (energy transfer) and now consider whether this helps to understand your answer to Q3.

Q6. When thermal equilibrium has been reached, what evidence is there that there is no longer a net flow of energy within the calorimeter?

Q7. Using the information from your simulation, calculate the energy “lost”* by the iron block. Use insert equation/scanned page to show your calculation and include units.

*Here we will use the word “lost” to represent the magnitude of the energy transfer.

Insert work here

Energy “lost” by iron block______________ cal

Q8. Using the information from your simulation, calculate the energy “gained”* by the water. Show your calculation and include units.

*Here the word “gained” represents positive change in the energy transfer.

Insert work here

Energy “gained” by cool water ______________ cal

The energy “lost” by the iron block and the energy “gained” by the water should be equal. If your numbers are different double check your calculation and conversions to ensure you get the same values.

In the simulation there are other materials. Let’s repeat the experiment using Silver.

Click the blue box “Reset”.

Choose silver as the solid of choice, then repeat the above steps. Notice that silver has a different specific heat than iron. Set the mass and temperature of silver to the same values you had for the iron block.

Q9. Convert your specific heat, csilver = _________ J/g.K    =   ______  cal/g.°C

Q10. Because silver has a different specific heat do you think the final equilibrium temperature will be lower or higher than for iron? (Highlight one)

Click blue box “Next”

Now set up the water in the calorimeter as you did above. Click Next.

Testing your prediction: click Start and wait for the water to reach its new equilibrium temperature

Record the final equilibrium temperature (with silver):     ________°C

Let’s try one more metal. Follow the same steps as above using the “Reset” and “Next” buttons.

For your solid choose Unknown metal II. Use the same settings the same as before. You will predict whether it is higher or lower than iron.

Do not check the “Show specific heat”

Here you will make a prediction about its value.

Q11. After the temperature has reached a steady value take a screenshot of your simulation and insert it here.

Insert screenshot here

Record the final equilibrium temperature (with Unknown metal II):     ________°C

Q12. Do you think Unknown metal II has a specific heat that is larger or smaller than that for iron? (Highlight one) Explain your reasoning here.

Activity 3 Theory

Here we review some textbook theory to test your prediction about the value of cMetal II (Q12). The 1st Law of Thermodynamics can be written as follows:

DU = Q – W             Equation 3

where, U is the internal energy of the system, Q is the net heat transfer into/out of the system, and W the net work done by the system. This is the Physics sign convention.) For the isolated block-water system, no work done is done, W = 0, so we have: DU = Q. For the case of constant specific heat, the change in the internal energy can be written as,

DU = mcDT => Q = mcDT                 Equation 4

which is where we get Equation 1 from the Introduction.

Considering the block of metal inside the water beaker as a combined, closed isolated system, no heat was added or lost to the outside, so the total change in the internal energy of the combined system is zero. This is how we know that (see shaded statement below Q8): ‘The magnitude of energy “lost” by the iron block and the energy “gained” by the water should be equal.’ Since, DU = Q, this implies that the net heat transfer as the hot block cools down and the water heats up, must add up to zero. Hopefully, you already saw this in your answers to Q7 and Q8.

Q13. Upon reviewing the above and using Equation 4, for the combined system of block+water, derive an equation for the final equilibrium temperature, your Equation 5. Show your work below. [Hint: This means that the block and the water will contribute their own Q to the equation.]

Insert work here

Q14. Now test the validity of your equation. Using the numbers you obtained for water-iron and water-silver above, calculate the two final temperatures using your Equation 5

Theoretical final equilibrium temperature (with iron):     ________°C

Theoretical final equilibrium temperature (with silver):     ________°C

If your numbers do not match the simulation values review your derivation of Equation 5 until you get the correct result.

Show any corrections here.

Insert your new derivation here, if necessary

You have just derived a very useful equation. To show you how useful it is, rearrange the equation to now solve for the specific heat of the Unknown metal II. This will allow you to predict the value of the unknown specific heat of metal II.

Q15. What is your value for:

cmetal II _____________ J/g.°C

Now convert to different units:

cmetal II _____________ cal/g.°C

Review your answer to Q12. You can now use the simulation to Show specific heat for Unknown metal II. Write down the simulation value here:

cmetal II _____________ J/g.°C

Does your number match the simulation? If not, correct your calculation and insert your new work here.

Insert your new calculation here, if necessary

Table 1: List of Specific heats for different solids.

Q16. Using Table 1 (right hand column), identify Unknown metal II (refer to Q14):

Activity 4 Melting Ice

Again, start this activity with a prediction:

Q18. Predict what will happen when you mix an equal amount of ice at -10 oC together with water at 10 oC. Describe any changes to the ice and water that might take place, in particular, do you think you will have the same amount of each after thermal equilibrium is reached?

Test your prediction. In this activity, you will use a simple simulation model to test your prediction. Navigate to the Specific Heat Online Simulation website.

You should see this:

Figure 2: Snapshot of the online simulation lab for Activity 4.

Read the text of the simulation page. This simulation sets the final temperature to be exactly 0°C. Extract the following information from the text:

cwater _________ cal/g.°C      Lfwater _________ cal/g.°C    cice _________ cal/g.°C

Set the slider for the “Initial mass of water” to read 100g. Record this value and the “Before” mass of ice:

Initial mass of water _________g    Initial mass of ice ____________g

Initial temperature of water _________ °C Initial temperature of ice ___________°C

Make a note of the “After” masses:

Final mass of water _________g            Final mass of ice ____________g

Q19. As the water cooled down, what happened to the ice? Explain in terms of energy transfer.

Q20. How much energy was “lost” by the water? Show your work here.

Energy “lost” by water ___________cal

Q21. How much energy did it take to raise ice from its initial temperature to the equilibrium temperature? Show your calculation.

Energy to warm melted ice ___________cal

Q22. Calculate the energy difference between the magnitudes of your values of the previous two questions. Show your calculation.

Energy difference _________________cal

[You can double check your calculations for Q1822 at the simulation webpage.]

Q23. Where did this energy (Q22) go or what did it do?

Q24. Take your energy difference (Q22) and divide by the mass of the ice that was lost (transitioned into the liquid phase). Show your calculation.

Q23. What are the units of this last quantity and what does it represent?

Q24. At the beginning of this lab (Q1) you were asked to rank in the order of how much energy is required from greatest energy to least energy, circling any that are equal.

(1)  Raising the temperature of 1 gram of water 1°C.

(2)  Raising the temperature of 1 gram of water 2°C.

(3)  Raising the temperature of 2 grams of water 1°C.

(4)  Raising the temperature of 1 gram of water from 0°C to 100°C.

(5)  Changing 1 gram of ice at 0°C to 1 gram of water at 0°C (melting).

(6)  Changing 2 grams of ice at 0°C to 1 gram of water at 0°C with 1 gram of ice at 0°C floating in it.

Make any corrections needed:

RANKING:               _____     _____     _____     _____     _____     _____ Pages (550 words)
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