Measurement of Specific Heat Capacity and Latent Heat of Fusion | PHYS 213, Lab Reports of Physics

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Physics 213 Laboratory

Measurement of Specific Heat Capacity and Latent Heat of Fusion

Purpose : Using calorimetry, the specific heat capacity of a maetal and the latent heat of fusion of water are to be measured.

Theory : When an object is raised or lowered in temperature the heat input ( or output )in calories is

Q = c m ∆ T

where c is the specific heat capacity, in calories / gram degree Centigrade. m is the mass of object, in grams, and T is the temperature change, in degrees Centigrade.

The method of mixing is used in the first experiment to determine the specific heat of a metal. Hot metal shot is added to a calorimeter cup containing cold water. The initial temperatures and the final equilibrium temperature are recorded. Then, from conservation of energy, the heat lost by the metal shot is equal to the heat gained by water and calorimeter:

c (^) shotmshot ∆ Tshot = c (^) water mwater ∆ Twater + c (^) calorimeter mcalorimeter ∆ Tcalorimeter

From this equation, if the specific heats of water and calorimeter are known, as well as all masses and temperature changes, the specific heat of the metal can be found.

Heat input causing a change of state from solid to liquid is given by

Q = LF m

where LF is the latent heat of fusion, in calories / gram, and m is the mass, in grams. In the second experiment, the latent heat of fusion of water is found by adding a sample of ice at 0 degrees C. to a calorimeter cup containing warm water. As the ice melts, the water cools to a final equilibrium temperature. Then, again by conservation of energy, the heat lost by the water and calorimeter is equal to the heat gained by ice:

c (^) water m (^) water ∆ Twater + c (^) calorimeter mcalorimeter ∆ Tcalorimeter = LF mice + c (^) water mice ∆ Twater from ice

( Note that after the ice melts, more heat is needed to raise the ice water from 0 degrees C. to the final equilibrium temperature.) By substituting for all masses, specific heats, and temperature changes, the latent heat of fusion of water can be calculated.

Procedure Experiment 1: The apparatus used includes a boiler for heating shot, shot holder, cork, dipping thermometer, calorimeter, 0 to 50 degree C. thermometer, supplies of metal shot, stirrer for calorimeter, and balance.

1. Fill the boiler half- full with water and start heating it.
2. Weigh a sample of metal shot and record its exact mass. If using aluminum shot, use about 80 grams. If copper or steel, use about 200 grams. If lead, use about 500 grams.
3. Put the weighed shot in the shot holder and place it in the top of the boiler. Put a cork on it and insert the dipping thermometer through the cork into the shot. Monitor the temperature until it is close to 100 degrees C.
4. Weigh the inner calorimeter cup ( without the fiber ring ) and record its mass. Add to the cup about 100 grams of water about 10 degrees C. below room temperature and reweigh it.
5. Insert the inner calorimeter cup, containing the stirrer and water into the outer beaker, with the fiber ring separating them. Place the wood cover over the calorimeter. Insert the 50 degree thermometer and the stirrer through the holes in the cover.
6. When the shot has nearly reached 100 degrees C., record the shot temperature and the temperature of the water in the calorimeter. Then pour the shot into the cold water in the inner calorimeter cup and close the calorimeter. Gently stir the water and shot. Watch the thermometer and note the highest equilibrium temperature of the water.

Calculations Experiment 1:

1. Write the symbolic heat lost = heat gained equation for the process. Substitute your experimental data into the equation and solve for the specific heat of the substance used. Compare your value with the standard value for the substance.

Procedure Experiment 2 : The apparatus used includes a Calorimeter, 0 degree C. thermometer, ice, and balance.

1. Record the mass of the inner calorimeter cup. Place in the cup about 200 grams of water at about 40 degrees C. Weigh the cup again and subtract to find the exact mass of the water. Put the inner cup into the outer beaker, and put on the lid with stirrer and thermometer protruding.
2. Select lumps of ice with a total mass of approximately 60 grams. Record the water temperature. Quickly dry the ice and add it to the water. Be careful not to splash any

water from the cup. Replace the wood cover and stir carefully; watch the temperature and as soon as all the ice has melted, record the equilibrium temperature.

3. Carefully remove the cover; shake into the cup all drops of water adhering to the thermometer and stirrer. Weigh the cup and contents to find the actual mass of ice used.

Calculations Experiment 2:

1. Write the symbolic heat lost equals heat gained equation for the process. Substitute your experimental data into the equation and solve for the latent heat of fusion of water. Compare it with the standard value.