Specific Heat Capacity and Latent Heat of Fusion
Introduction
Heat is the transfer of energy due to a temperature difference. When an object gains or loses energy through this mechanism, we might observe a temperature change or a phase change (or both).
Specific Heat Capacity
Temperature change is a symptom of an object having gained or lost microscopic kinetic energy as a result of heating. When this occurs, there is a mathematical relationship between heat and temperature:
[1] Q = mcΔT
Q = heat (J)
m = mass of the substance (kg)
c = specific heat capacity (J/kg/K)
ΔT = change in temperature (°C or K)
The specific heat capacity is an empirical, material-dependent quantity that will be a focus of this lab.
Latent Heat of Fusion
A phase change (melting or freezing) is a symptom of an object having gained or lost microscopic potential energy as a result of heating. The energy required to induce a phase change can be quantified:
[2] Q = ±mLf
Q = heat (J)
m = mass of the substance (kg)
Lf = latent heat of fusion (J/kg)
The plus sign indicates melting while the minus sign indicates freezing. The latent heat of fusion is an empirical, material-dependent quantity that will be another focus of this lab.
Calorimetry
The general technique you will use to determine specific heat capacity and latent heat of fusion is called “calorimetry”. Basically, this means keeping track of heat. For an isolated (well-insulated) system, the total heat will be zero:
[3] ΣQ = 0
Equations [1] and [2] can be used in equation [3]. The specific implementation will depend on the experiment.
Experimental Procedures
Specific Heat Capacity of Metal
1)Partially fill a beaker with hot top water. Heat the water on a hot plate.
2)Measure the mass of a metal solid and place it in the hot water.
3)Measure and record the mass of a cup.
4)Partially fill the cup with cold tap water and measure the mass again. Calculate the mass of the water.
5)Place thermometers in both the hot water and cold water.
6)Wait a few minutes and record the temperatures of the hot and cold water.
7)Use the tongs to quickly move the metal solid from the hot water to the cold water. Try not to have any water drops on the metal solid. Cover the water with a lid.
8)Shake the cup gently on occasion. Monitor the temperature of the water until it is steady. Record this temperature.
9)Use calorimetry to derive a symbolic equation for the specific heat capacity of the metal in terms of temperatures, masses, and the accepted value for the specific heat capacity of water, (4190 ± 15) J/(°C kg). Show your equation to your instructor.
10)Use your equation to calculate the specific heat capacity of the metal. Compare this to the accepted value for this particular metal.
11)Repeat the above steps two more times. You might vary the masses, the metal, or the temperatures.
Latent Heat of Fusion
12)Measure and record the mass of a cup and lid. Fill the cup about half full of hot tap water and measure the total mass with the lid placed next to the cup. Calculate the difference to obtain the mass of the water.
13)Measure and record the initial temperature of the water once the temperature is fairly steady.
14)Using a towel, dry off 5 to 10 ice cubes, put them in the hot water, and cover. Occasionally gently shake or stir the cup until the temperature is steady. Record the final equilibrium temperature.
15)Measure the final mass of the cup and water. Calculate the difference between this value and your previous measurement to obtain the mass of the ice cubes.
16)Use calorimetry to derive a symbolic equation for the latent heat of fusion in terms of temperatures, masses, and the accepted value for the specific heat capacity of water. Show your equation to your instructor.
17)Use equation [3] to calculate the latent heat of fusion for water. Compare your experimental result to the theoretical value of (3.34 ± 0.01) E5 J/kg.
18)Repeat this experiment two more times with a different initial temperature of water (not more than 50 °C, different amount of hot water, or different number of Ice Cubes.
Note: you can use °C for temperature even though it is not SI. This is because the formulas are dealing with temperature changes, not absolute temperatures.