Thermoelectric cooler & Carnot Engine

We started the day with understanding about thermoelectric cooler. There's two cups on each side of the hypnodisk. Each is to be filled with hot water and iced water. The purpose of this machine is to convert the difference in temperature into electricity. The placement of the water does not matter, it only makes the hypnodisk spins the other way.

when hypnodisk is taken off and replaced with power, it then does the opposite; it converts electricity into two different temperatures as we can see in some of refrigerators.

We knew from the heat formula about heat capacity, but we did not go deeper into it. So today, we learned about the understanding of heat capacity. To find heat capacity when heat and change in temperature is given, we just divide them. When molar is involve, we just multiply them by the inverse of mole.

In isochoric, we knew from the past lecture that internal energy is 3/2 PV or 3/2 NKT. Since the volume is constant, means that there is no work. This leaves change in energy equals to heat. When we set these equations equal to each other, we found heat capacity to be 3/2R, which we also know this to be noble gasses from chemistry class.

We know that Cp=Cv+R from ...

We can replace R into Cp-Cv in ideal gas law. Given that PV= P*delta V + V*delta P. By combining these two equations, we found their relationship as below.

By deriving it again with the ideal gas law, can now find that by adding V*delta P/P* delta V and Cp/Cv, they become zero.

By separating pressure and volume on each side of the equation and integrating them. We found the relationship of them to be inverse as below.

Work, as we knew, to be efficient has to be heat in minus heat out. We knew that power is work divided by heat in. By collaborating these equations, we found the efficiency equation to be 1- heat in/heat out. Given some numbers as below, we calculated the efficiency using the equation that we have derived.

The relationship between heat in and heat out is proportional to temperature in and temperature out.

In a car engine, to make it efficient, we would want the radiator to be cooled when the engine heats up.

Lastly, we learned about engine. There are four process in working engine, which are intake, compression, power, and exhaust. During intake, the intake valves open, and the piston moves down and intake valves close. During compression, all valves are closed, piston moves up, and the gas is ignited. During power, there's explosion, piston moves down to increase volume. During exhaust, piston moves back up to create pressure, and exhaust valves open.

From those four processes, we make a graph of Pressure vs. Volume and connect them. The graph looks like a parallelogram. The enclosed graph shows the amount of work done in the engine.

There are three ways to increase the work, which is shown below.