Procedure:
First we put a casserole with water on the electric cooker. We turned it on and waited to the water started boiling. Then we put our lead ball into the water and left it there until it was reasonable to assume that it had the same temperature as the water. We measured the temperature in the water. While we heated the lead, we filled a calorimeter with water and measured the weights we needed and then measured the temperature in that water. Then we placed the lead ball in the calorimeter and followed the change in temperature. It increased rapidly at first and then slowly. We decided that the temperature we had when the increased slowed down, was the thermal equilibrium. Since we used cold water, the surroundings would make the closed system gain heat after the ball and water had the same temperature.
Observations and measurements:
To measure temperature in this practical, we used a simple thermometer with an uncertainty of +/- 1˚C. To measure weight we used a simple electronic balance with an uncertainty of +/- 1 g. However, since we will convert the mass to kg in the calculations the uncertainty will be immensely small so we will not consider it.
Calculations:
The heat required to increase the temperature in the calorimeter:
H = mw x cw x ΔT + mal x cal x ΔT
Hmin = 0.093 kg x 4186 x 4 + 0.039 kg x 900 x 4 = 1697.6 J
Hmax = 0.093 kg x 4186 x 8 + 0.039 kg x 900 x 8 = 3395.2 J
H = 0.093 kg x 4186 x 6 + 0.039 kg x 900 x 6 = 2546.4 J +/- 848.8 J
The heat capacity of lead:
H = mPb x cPb x ΔT
CPb = H/ (mPb x ΔT)
CPb-min = 1697.6 J / (81˚C x 0.199 kg) = 105.3 J kg-1˚C-1
CPb-max = 3395.2 J / (77˚C x 0.199 kg) = 221.6 J kg-1˚C-1
CPb = 2546.4 J / (79˚C x 0.199 kg) = 162.0 J kg-1˚C-1 +/- 59.6 J kg-1˚C-1
Conclusion and evaluation:
If you compare the value we got with the literature value, we see that it is in the proximity but slightly too high. This indicates that the procedure and calculations done are good and that they work in theory. The reason why our result was to high is probably that the closed system we used gained heat from the surroundings since the water in the calorimeter was colder than the room temperature when we began. The only way to escape this source of error with our available equipment would be to isolate the closed system better. If we had available resources it might have been possible to create a close room where we could place the calorimeter. We could have a digital thermometer in the calorimeter that was connected to a very powerful fan that automatically increased of decreased the temperature in the room to the same as in the calorimeter. This is only an idea and I doubt it would be possible to do this at school.
Another thing about this experiment is that we get a too high uncertainty in the temperature. This played an especially large part in the change in temperature in the calorimeter. The percentage uncertainty was as high as 33 %. If this had been smaller, we could have had a drastically smaller uncertainty in the answer. It would be possible to do this by simply using an electronic thermometer.
