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The Mechanical Equivalent of Heat


As an application of the principle of conservation of energy we're going to be converting mechanical energy into thermal energy. And the way we're going to do that is by increasing the thermal energy of some lead and some small lead shot in this Styrofoam cup here. The way I'm going to increase the thermal energy is by lifting that lead and then letting it drop. As it drops the initial gravitation energy will be converted first into kinetic energy and when it stops by running into a platform that kinetic energy will be mostly converted into thermal energy of the system. We're going to measure that increase in thermal energy by measuring the change in temperature of the system. So the principle that describes this experiment is that the work done on a system by external forces is equal to the change in energy of that system. In the example we're talking about that energy change will be thermal energy. The work done will be done by me I'm going to be lifting the lead to a higher location giving it some gravitational energy. The gain in energy when I lift it is simply mgh, m being the mass of the lead g being the gravitational constant and h being the height that I lifted it. As you'll see I'm actually going to lift the lead to the same height multiple times so I'm going to do this n times but the total work of the system will be mgh. That's the work done by the external force. On the right hand side will be the change in energy of the system. We can write an expression for the change in thermal energy by using the specific heat of lead. The terms for the specific heat will be the mass of the lead times the specific heattimes the change in temperature of the lead. What we're going to actually measure will be the change in temperature so I can find an expression for the predicted change in temperature simply by solving for ΔT. The mass of the system simply cancels out in this experiment. So all I need to know is the number of times I lifted it, g. the height I lifted it, and the specific heat of the lead.

Alright let's do our experiment now I have my lead in the Styrofoam cup, a good insulator which is more or less at room temperature. The temperature for this experiment will be measured by this thermal cup which will read out on this laptop screen. We're just going to test right now that the temperature of this lead is room temperature by putting the thermal cup in there and you can see that the room temperature is 23 and 24 degrees Celsius. And lead is more or less at the same temperature. To start the experiment I am actually going to cool the lead to several degrees below room temperature and at the end I'm going to ask you to tell me why I'm doing that. So to cool it off I'm going to pour it into this aluminum cup and then put the aluminum cup into a cold water bath for a few seconds. Aluminum is not a good insulato;r it is a good thermal energy conductor. So the lead being initially at a higher temperature than the water will loose thermal energy through the aluminum cup. Okay so the lead has cooled off for a couple of minutes, and the temperature of the lead is about 15 degrees. Okay so to start the experiment now I'm going to poor the lead into this cardboard tube. And mix it. Alright that was 300 times, now I'm going to let the lead shot out pour it into the Styrofoam cup and then measure the temperature again with the Styrofoam cup. And that temperature is now about 26 degrees Celsius. So now, our initial temperature was about 15 degrees Celsius and the final temperature about 26 degrees Celsius. Now you can now compare that change in temperature with the change that would be predicted by the conservation of energy principle. So I'm going to leave that up to you. The numbers you need to know I already told you: the numbers of times I lifted up, g is a number you know, the height will take to be just the length of this cardboard too and I'll measure this for you pretty close to 54 centimeters 53.6 a little bit more precisely. The last number you'll need to know is the specific heat of lead at room temperature that's a number I'm going to let you look up to compare. And you'll be giving your answer to the prediction and comparing that to the measurement in the assignment to follow up to this video. Another thing I would like you to think about is what was the reason that we started the lead at the temperature below room temperature.

Now what we have just done is seen a conversion of mechanical into thermal energy and we've seen that by lifting it and letting it fall to raise it's temperature.

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