Entropy and Refrigerators

On September 16th, 2014, Physics 4B learned about the chaotic entropy and the efficiency of refrigerators and air conditioners.

Entropy:

Entropy is defined as the amount of energy needed to heat up a gram of water by one degree Kelvin. Or Q/T. The units for entropy is Joules over Kelvin. But there is a way to make entropy unit-less and that is dividing the equation by constant k.

We also have listed some examples of change in entropy in real life applications.

Stripling Engine Cycle:

The Stripling Engine's efficiency, although built before, is actually similar to that of a Carnot Engine. It relies on the heat applied on the bottom of the engine and the iced top to move the piston. The two different temperatures on both sides means that the piston movements is relied on the change of pressure. Below are some pictures of the Wanckle engine.

Below is a simulation of the process of a Wanckle engine.

As stated before, the efficiency is pretty high but one would prefer not to have it in their cars because that would mean the engine would have to be enormous.

Refrigerators:

Next, we were asked to find the output heat of a refrigerator.

If one were to look at the packaging of an air conditioner, the efficiency is measured in BTU/hr/W. But what is a BTU in Joules? We were asked to find the conversion factor. 1 BTU is about 1055 Joules.

Keeping that in mind, how many Joules per second are in 12000 BTU per hour? Approximately 3516 Joules per second.

Reversible Engine:

We were then given two blocks of water and ice with different temperatures and were given the task to find the final temperature when both blocks were fused. Assuming the change in entropy in the system was zero, the final temperature of the blocks when fused was found to be 46.1 degrees Celsius.

We then found an equation for work.

And found a new equation for efficiency for a reversible engine.

We were then asked a trivial question: How many flights of stairs would a person be able to climb per minute? We found work to be 4900 J and one horsepower to be about 760 Joules per second. After converting, a human would be able to climb 9.3 flights of stairs per minute. Although, thinking about it realistically, it is not possible even with a burst of energy since humans cannot sustain energy for a long period of time during extensive exercise.

We were then asked to find the coefficient of power for refrigerator running at three-fourths of horsepower.

 The goal was to find how long it would take for a freezer to freeze 4.2 kg of water. Theoretically, if the freezer was to run at full power for 13.7 mins, it would be possible.

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.

Below is simulation of the inside of an Otto Engine.

Heat Engine

This is a summary of what my lab group and I did in Physics 4B on September 9th, 2014.

Chimney Effect:

The first demonstration was that of a candle that was lit inside of a graduated cylinder. My lab group and I thought the fire will stretch upward attempting to gain more oxygen gas to burn but the fire actually extinguished pretty quickly. This was because not enough oxygen was flowing down into the graduated cylinder. 

As you can see in the clip below, the fire was almost immediately extinguished as it entered the graduated cylinder.

But what if we inserted a small PVC pipe and place it right above the flame?

My lab group and I predicted that the PVC pipe will create an air current allowing oxygen to flow into the cylinder through one side and the CO2 through the pipe. Our prediction was correct.

As the "chimney" is put in place, the fire continues to burn.

And the flame became dimmer as the "chimney" began to grow farther and farther away from the flame.

Next, we were asked what would happen to the candle's flame if it was put inside a gallon jug with a rubber stopper as the cork and in free fall. My lab group and I thought because it was a closed system, the flame would be unaffected; however, we were wrong. The flame actually became dimmer because convection no longer played a role in the system and the flame was fueled by diffusion instead.

We were told to give a real life example of negative work, which means that there is no heat involved in the system. We came up with the compressing of a spring. Because delta internal energy is equal to negative work in this system, the internal energy is increasing as the potential energy goes up in the system.

State Variables and Ideal Gas Law:

As a class, we visited a site that explained Isobaric, Isovolumetric, and Isothermal processes. We answered six questions regarding the processes; three of which we were told to draw the graph of the different processes. And then, with given values, we found various components of the gas (pressure and volume) using the definitions of the three processes and the Ideal Gas Laws.

Then, we were asked to identify what processes the four graphs represented on a PV-plane. Graph A was isobaric because pressure was constant. Graph B was isochoric because volume was constant. Graph C was speculated to be adiabatic because the slope was a lot more steeper than graph D. Graph D was speculated to be isothermal because the slope was less steep than graph C.

Heat Engine:

Below is a demonstration of what a heat piston does. When the heat was applied, the syringe acted as a piston and began to emulate that of a piston by going up and down. In this situation, there was no work being done but heat was being applied.

We were given a question regarding a water tank. The first part of the question was to identify the work being down by the gas on the tank. After some derivation, we determined the equation for the work done by the gas to be the pressure of the air times the volume of the tank times the natural log of 4 since the water only rose to fill three-fourths of the tank leaving one-fourth of the tank of air.

Next, we were asked to identify the work being done by the pump. Here, the equation was the change in mechanical energy plus the absolute value of the work done by gas subtracted by the work done by the air.

This apparatus measured gauge pressure, volume of the cylinder, and the temperature within the cylinder. Professor Mason changed the volume of the cylinder from 50 cc to 30 cc and then asked us how much work he did on the system. The answer has to be small because it did not take him a lot of energy to change the volume of the apparatus.

After identifying the knowns, we determined the equation of the isothermal work to be initial pressure times initial volume times the natural log of final volume over initial volume.

Efficiency:

Below is a cycle that my lab group and I created to describe the process of a rubber band engine.

The Greek letter for efficiency is eta (or e) and that is equal to the work done divided by the energy inputted to the system. If we recall one of our work equations, it was energy input minus energy output. If we substitute that into our efficiency equation, we get efficiency equal to one minus energy output over energy input. The perfect efficiency of a system would be when either energy output or energy input is equal to zero but that is almost impossible to achieve.

Analyzing the Cycle:

Below is the answer to the questions scribed in our lab manual. First, we drew the PV diagram of a cycle, which turned out to be a rectangle because temperature was kept constant.in parts A and C of the graph, work was being done by the gas and on the gas respectively. Also, in part A of the graph, the heat energy is transferred to the gas from a reservoir and in part C of the graph, the heat energy is being transferred from the gas to the reservoir.

This system turns out to be 6% efficient, which is not very efficient.