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Introduction
Heat is the transfer of energy between a system and its environment because of a temperature difference between them. When two objects in thermal contact with each other come to the same temperature, the two objects are said to be in thermal equilibrium. No heat flows between objects in thermal equilibrium.
Every substance requires a unique amount of energy (Q) per unit mass (m) to change the temperature (T) of that substance by 1° C. This unique quantity is called the specific heat (c). The amount of energy it takes to change a material’s temperature is given as:
Q = mc∆ T (1).
Changing the phase of a material also requires energy. The amount of energy (Q) you must add or gain to change the phase of 1 kg of material is called the latent heat. Each type of transition for a specific material will have a different latent heat. When changing phase from solid to liquid or vice versa, this quantity is called the latent heat of fusion. The energy required to melt or freeze a mass (m) of material is:
Q = lf m (2).
When changing phase from liquid to gas or vice versa, this quantity is called the latent heat of vaporization. The energy required to vaporize or condense a mass (m) of material is:
Q = lv m (3).
In this lab, you will investigate objects in thermal contact coming into thermal equilibrium and use this to determine the latent heat of fusion for water and the specific heat for aluminum.
The principles in this lab should reinforce the following concepts:
- Heat and specific heat
- Calorimetry
- Latent heat and phase changes
Experimental Procedures
Activity 1: Determining the Latent Heat of Fusion for water
Equipment: calorimeter cup, thermometers, water, ice, beaker.
(1) Measure the mass of the cup [MCUP]. Record this value in Table 1 on the Data Analysis sheet. Convert from grams to kilograms.
Lab 1: Heat and Calorimetry
(2) Add warm water to the cup until it is approximately 1/2∼3/4 full. Measure the mass of the cup + water [MCUP+WATER]. Record this value in Table 1 on the Data Analysis sheet. Convert from grams to kilograms. (3) Calculate the mass of warm water [MWATER]. Record this value in Table 1 on the Data Analysis sheet. Convert from grams to kilograms. (4) Measure the mass of the other cup. In the second cup, add a small amount of ice as discussed in class. Measure the mass of the ice + cup and subtract the mass of the cup to determine the mass of the ice [MICE]. Record this value in Table 1 on the Data Analysis sheet. Convert from grams to kilograms. (5) Place a thermometer in the warm water and measure the initial temperature of the system [Ti(warm water)]. Record this value in Table 2 on the Data Analysis sheet. (6) Use a second thermometer to measure the initial temperature of the ice [Ti(ice)]. Record this value in Table 2 on the Data Analysis sheet. (7) Add the ice to the warm water. Mix the ice and warm water until the ice completely melts. As soon as the ice is totally melted measure the new temperature of the system [Tf(system)]. Record this value in Table 2 on the Data Analysis sheet. (8) Complete the Data Analysis sheet for Activity 1 before moving on to Activity 2.
Activity 2: Verify the Specific Heat of Aluminum
Equipment: calorimeter cup, thermometers, water, ice, beaker, hot plate, aluminum rod.
WARNING: Read through all instructions before beginning. You will be working with boiling water that can scold you if you are not careful.
(1) Measure the mass of the cup [MCUP]. Record this value in Table 5 on the Data Analysis sheet. Convert from grams to kilograms. (2) Add cold water to the cup until it is approximately 1/2 full. Measure the mass of the cup + water [MCUP+WATER]. Record this value in Table 5 on the Data Analysis sheet. Convert from grams to kilograms. (3) Calculate the mass of the cold water [MWATER]. Record this value in Table 5 on the Data Analysis sheet. Convert from grams to kilograms. (4) Measure the mass of the aluminum rod [MAl]. Record this value in Table 5 on the Data Analysis sheet. Convert from grams to kilograms. (5) In a second cup place the aluminum rod with the string outside of the cup and cover completely with water. Place the cup containing the aluminum on the hot plate. Heat the water until boiling. As the aluminum is heating, place a thermometer in the cup of cold water. Measure the temperature right before completing the next step [Ti(cold water)]. Record this value in Table 6 on the Data Analysis sheet. (6) When the water begins to boil the aluminum rod should be in thermal equilibrium with the boiling water (100 °C). Therefore, Ti(aluminum) = 100 °C. (7) Being very careful, remove the aluminum rod from the boiling water using the attached string and place the rod in the cold water. Stir and allow the system to reach an equilibrium temperature. Record the final temperature of the system [Tf(system)]. Record this value in Table 6 on the Data Analysis sheet. (8) Complete the Data Analysis sheet for Activity 2.
- Using Eq. 1 and your data, calculate the amount of energy lost [Qwarm-water] in lowering the temperature of the warm water to the final equilibrium temperature [Tf(system)]. Record this value in Table 3. Be careful with the sign! Show your calculation below.
- Using Eq. 1 and your data, calculate the amount of energy [Qwater-ice] it takes to raise the temperature of the melted water-ice from 0 °C to the final equilibrium temperature [Tf(system)]. Record this value in Table 3. Show your calculation below.
- Write an expression for the conservation of energy for this system using Qice, Qwarm-water, Qwater-ice and the energy necessary to completely melt the ice [lfMICE from Equ. 2].
- Solve for the latent heat of fusion, lf, and calculate its value using your data from Table 3 and MICE. Record this value in Table 4. Show your calculation below.
Energy (J)
Qice
Qwarm-water
Qwater-ice
Table 3: Energies associated with reaching equilibrium.
- Calculate the percent error from the known value using the following equation:
× 100 %
K
K f l
l l Error
where lK is the known value for the latent heat of fusion for water [33.3× 104 J/kg]. Record this value in Table 4. Show your calculation below.
Activity 2: Verify the Specific Heat of Aluminum
Table 5: Masses of the system’s components.
Mass [g] Mass [kg]
MCUP
MCUP+WATER
MWATER
MAl
Table 6: Initial and final temperatures of the system.
Temperature [C°°°°]
Ti (cold water)
Ti (aluminum)
Tf (system)
lf [J/kg] Percent Error [%]
Table 4: Latent heat of fusion for water and percent error from known value.
