3/12 Carnot Engine and Otto Engine

This is an example of a thermal engine where one cup contains ice cold water and the other cup contains hot water. The hot water naturally wants to transfer its energy to the cold water and the engine in the middle spins based  off of this energy transfer.

This is the thermal engine in spinning in the direction of the heat transfer. Since the heat goes from the right cup to the left, the spinner spins counter clockwise.

This is where the cups are switched and the spinner spins in the clockwise direction.

With the cups removed, the engine is attached to a power supply and takes away heat from one metal leg and transfers it to the other. The student is touching both sides to confirm the the temperature.

This is our predictions for how the thermal engine would behave in both the experiment with the cups and with the power supply.

We calculate for the Cv and its relationship with R using the first law of thermodynamics.

We calculate for how moles and change in temperature relate to Cp, Cv, Pressure, and volume. We take the derivative of P delta V and use product rule which is why our numerator is not P delta V.

We derive a relationship between change in volume and change in pressure to set up a differential equation relating the two rates. We take the definite integral of pressure and volume and use algebra to cancel our variables and ended up with (ΔP/P) + (ΔV/V)(Cp/Cv)=0

Given that , we were asked to prove that  where gamma = 5/3. After we proved it, we found how those equations can be used to calculate work.

We are given an adiabatic problem where we use our derived work formula and plug in numbers to find the work done by the change in volume of the system.

Using the equations we derived in class, we were given a scenario where we have a Carnot engine where adiabatic and isothermal reactions occurred in one cycle. Between each of the 4 points, we had to calculate the Work, Internal Energy, and the Heat transferred and the efficiency of the engine.

This is a model of how the Otto engine operates.

This is the combustion part of the cycle as represented by the red glowing light. 

We answered the question of how to increase efficiency by answering that we could increase the difference of the cold and hot reservoirs by adding more radiators for more cooling. We answered the question of how to physically altar an engine to  increase work done by an engine. We were asked to draw the 2 additional degrees of freedom gained when a diatomic molecule is split into two.

Summary: We learned how different types of engines operate to create work from heat transfer. We learned equations that included Constant Volume(Cv) and Constant Pressure(Cp) and derived their relationship with the ideal gas law constant, R, and how it is conserved in a thermal reaction. We discussed different types of engines such as the uranium thermal engine used in rovers exploring space and the engines of old "Otto"mobiles.