Among the most tough (and most essential) experiments within the historical past of physics had to do with making connections between totally different ideas. What in regards to the connection between objects shifting round (kinematics) and objects altering temperature (thermodynamics)? That was a tricky one. It is known as the mechanical equal of warmth and it was explored in 1868 by James Joule.
The essential concept was to have a mass that strikes down due to the gravitational force. This mass is connected to a string that connects to a spinning paddle in a container of water. Because the mass strikes down it spins the water and provides vitality to it—hopefully growing the temperature. The change in gravitational energy of the mass ought to be equal to the change in thermal vitality of the water.
OK, we really already know this relationship. But it surely’s nonetheless enjoyable to reproduce it. To try this, first we’d like to know in regards to the totally different types of vitality. First there’s the gravitational potential energy. In case you are close to the floor of the Earth and elevate a mass, there shall be a change in potential energy. The quantity of vitality change depends upon the mass of the thing, the peak moved, and the native gravitational area (g). We are able to write this as:
On Earth, the gravitational area has a price of about 9.eight Newtons per kilogram. Which means should you take a textbook (with a mass of about 1 kilogram) and raise it from the ground to the desk (about 1 meter), the e-book’s potential vitality would improve by about 10 Joules. That vitality had to come from you—the lifter.
The second type of vitality to take into account is thermal vitality. That is the vitality related to the temperature of an object. The change in thermal vitality of an object depends upon three issues: the thing’s mass, the change in temperature, and the precise warmth capability (which depends upon the fabric).
The precise warmth capability (C) is the quantity of vitality it takes to change 1 kilogram of the fabric by 1 diploma Celsius. Completely different supplies have totally different thermal properties (water is just not the identical as copper) in order that they’ve totally different values of C. Oh, and simply because we’re going to want it quickly—the precise warmth capability for water is 4184 Joules per kilogram per diploma Celsius and copper is 385 J/kg/°C (sure, water is loopy excessive).
So, this is what I am going to do. It is related to the Joule experiment, but additionally barely totally different. As a substitute of a paddle that interacts with water, I’ve two copper cups that rub towards one another. It appears to be like like this.
The underside cup is held stationary and the highest cup spins and rubs towards the underside cup, inflicting friction. Some water is added into the highest cup in order that the temperature may be measured. A string wrapped across the prime cup goes over a pulley to a vertical hanging mass. Because the mass strikes down, it spins the cup. Then I simply want to calculate the change in gravitational vitality (based mostly on the peak) and the change in thermal vitality (for the cups and the water).
There’s a temperature sensor within the water and in addition a rotational movement sensor on the pulley. Which means I can constantly report each the gap the mass strikes in addition to the temperature. Here’s what my setup appears to be like like. Oh, there’s a mass and a wooden plate on prime to hold all of it collectively.
With that, I get the next knowledge.
Calculating the change in gravitational potential vitality is pretty straightforward. The mass was 1.three kilograms, moved by a top of three.6 meters. This offers a lower in gravitational potential vitality of -45.86 Joules.
For the rise in thermal vitality, I in fact want the change in temperature. It went from 24.9 C to 25.1 C. Sure, that is a reasonably small change in temperature. So as to calculate the change in thermal vitality, I would like the precise warmth capability for the 2 supplies (water and copper). I additionally want the lots. The water was 20 grams (0.02 kg) and the copper (for each cups) was 0.261 kg. The change in thermal vitality for these two supplies mixed was 36.86 Joules.
Increase. That is pretty shut. It exhibits that the full change in vitality for the system consisting of the Earth, the falling mass, the copper and the water was shut to zero. There was no work achieved on the system so there was no change in vitality. Sure, the change in thermal vitality was barely lower than the change in gravitational potential vitality. That is seemingly due to some vitality loss as stuff apart from the copper and water additionally warmed up a little bit. Nonetheless, it is a fairly good experiment.