Download Mechanical Equivalent of Heat

PH111 Recitation
Mechanical Equivalent of Heat
Introduction
When an object is near the surface of the earth at a height, h, the earth and object system has a
potential energy of the following:
[1] U = mgh
According to the law of conservation of energy, this potential energy is converted into kinetic energy
when the object falls. If this object comes to rest through collisions that are not perfectly elastic, this
kinetic energy, a form of mechanical energy, is converted to thermal energy of the object (and its
surroundings). This change from mechanical energy to thermal energy is equivalent to the thermal
energy gained from heat.
The relationship between temperature and thermal energy is given by the calorimeter equation:
[2] ΔEth = mcΔT
ΔEth = change in thermal energy
m = mass of the substance in kg
c = specific heat capacity in J/(C° kg)
ΔT = change in temperature in C°
Note that this formula assumes that the energy input does not lead to a phase change.
The above two formulas can be set equal to one another and solve for the change in temperature. In
other words, we can determine the rise in temperature of something dropped.
[3] ΔT = gh/c
If we drop something multiple times, then the formula should be multiplied by N, the number of times
something is dropped.
[4] ΔT = Ngh/c
Experimental Procedures
1) Measure the inside length of the tube.
2) Calculate the theoretical change in temperature using equation [4]. The specific heat of lead is
130 J/(C° kg). The specific heat of steel is 452 J/(C° kg).
3) Pour some shot (about 500 grams or so) into a styrofoam cup.
4) Measure the initial temperature of the shot.
5) Place the shot in the tube and screw the cap on. MAKE SURE that the cap is screwed securely
on or you will have to clean up a lot of lead shot when it spills on the floor!
6) Quickly invert the tube and let the shot fall to the bottom. Repeat this procedure so that the
lead shot fall a total of 100 times.
7) Pour the shot back into the cup and quickly measure its final temperature before it cools down.
8) Calculate the experimental change in temperature and compare it to the theoretical value.
9) Repeat the experiment a few times using a different quantity of metal, a different number of
turns, or a different substance.