Physics 4B slim: Heat Engines and PV Diagrams

On September 11th, 2014, Physics 4B class of Mount San Antonio College tackled the topic of the cycles of heat engines and their PV diagrams.

Heat Engine:

Below is a picture of an engine that is not meant to hypnotize but to demonstrate the power output of a heat engine powered by a hot water reservoir and a cold water reservoir. This however, is not as efficient as one would hope.

Professor Mason even had to blow torch the hot reservoir side to give it a kick start because the initial temperature of the hot water was not sufficient to start the engine.

Next is a picture of the same engine except, it is now being powered by a source of electricity.

Analyzing a PV Diagram:

Below is a demonstration Professor Mason did to show us how a piston worked. He used the Logger Pro program to also show us graphically.

The result is shown below:

We were asked to identify what kind of compression each part of the graph was going through.

We were then asked to find the net work of the entire graph. We found the net work by finding the area under the graph geometrically. Our numbers were not as accurate because it was difficult to determine the actual numbers.

We then found the specific heat in an adiabatic expansion.

And then, we related it to the Ideal Gas Law.

Afterwards, we combined the result from the first two derivations to get delta P over P plus C_p over C_v times delta V over V to equal zero.

If the limits are of small variables, the equation above can be integrated from initials to finals to yield the result below. And if we relate it once more to the Ideal Gas Law for temperature, we get the result also stated below. Notice that the exponents are different for a monotomic gas and a diatomic gas.

We then found the equation for work in an adiabatic expansion.

With the found equation, we found the work of a given problem. The work for that adiabatic expansion was 1246 J.

Carnot Engine Cycle:

We then focused our attention to the Carnot Engine Cycle, the most theoretically efficient engine. Using the First Law of Thermodynamics, we were asked to find the delta internal energy, work, and heat of the graph of the Carnot Engine Cycle graph. We then also found the net work and the efficiency of the sample Carnot Engine.

Otto Engine:

Below is an example of an Otto Engine. This is a more common engine (found in cars) but it is no where near as efficient as the theoretical Carnot Engine.

Professor Mason is explaining how the Otto Engine works.

Although brief, we saw that the piston moved up and down. As the piston moves down, it allows gases to escape or enter the piston and when the piston moves up, it compresses the gas and causes a reaction with the spark plug, which results in work, heat, and power.