(9/18/14) Entropy and Cycles

In this lab we went more in depth into heat engines, bringing up the idea of entropy, the assortment of the system, and did experiments to get better acquainted with the idea of entropy.

Class Activity: Turning Green into White

Green water turned white

We started the lab by doing two different types of simple experiments. The first experiment involved burning paper, while the second experiment had a green substance (on the left) enter into the clear substance (on the right) and have it turn completely clear. The idea of entropy, or randomness came into place as we understood



Defining Entropy

Our responses to defining ΔS and examples of  changing ΔS

Here we are given a quantitative form of entropy, notated as  ΔS to be ΔS= ΔQ/T, where Q (in Joules) is the heat and T is the temperature (in K)
We were asked to break down the units of entropy as far as we could, which eventually becomes kgm^3/Ks, to get a better understanding of what entropy is in terms of what we learned from previous physics classes
We then were asked to find examples of a change of ΔS, which we noted as the following:
1) Opening a soda can (gas molecules leaves the soda, increasing ΔS)
2) Diffusing of gas
3) Spilling of water (composition of molecules get scattered, increasing ΔS)

The TS graph

A graph of isothermal and isoentropic process in a T vs S graph

We then focused on learning a new style of graphs in correlation to ΔS, the T vs S graph. This graph allows us to see a cycle in relationship to the P vs V graph style that we have learned previously. Furthermore, we have learned how to convert a PV graph to a TS graph if need be.
We also learned two new cycles from this graph, the Stirling Cycle and the Brayton Cycle

A picture of our example Stirling Engine

We learned more about how a Stirling Engine via experimentation. By taking a Stirling engine, along with hot water (hot reservoir, below the engine)  and ice cubes, we observed how the rudder spins, understanding that heat is moving within the system, allow energy to flow.

Stirling Engine Experimentation

Efficiency Calculation

Additionally, we discovered that a Stirling Engine has the same efficiency as a Carnot Engine, from which, we can then find the efficiency of the Stirling Engine in this case.







Understanding Heat Pumps and Refrigerators
A class example came, in which we had to calculate the COP (coefficient of performance) of both a refrigerator and heater

Finding watts and COP

 This example showed us how to calculate  the amount of wattage needed to use a heater and an air conditioning unit, knowing  its COP and the amount of wattage that was placed into the system

It is to note that in both cases of the heater and air conditioning unit, the amount of wattage let out is of an ideal amount, since they both released more wattage than what was originally placed in (2700W)

Finding Efficiency within an air conditioning unit:
An interesting question was raised up about how much efficiency does a standard air conditioning unit has. Prof. Mason stated that no company will ever release that kind of data, for fear of what to come. Therefore, as the future physicist and engineers that we are, we were asked to convert BTU (worthless units, lb/°F) to a unit that we know it as, Joules

Our conversion factor

Finding the conversion between BTU and Joules required a few steps. We needed to convert BTU to g/°C, which is the definition of a calorie. Once we converted the BTU to calories, we can then convert it to Joules, assuming that a calorie is the amount that it takes for one gram of water to change by one °C, in which we obtained the answer to be about 1200J

Finding Watts

It doesn't stop there, however, as we now have a definitive conversion between BTU and Joules, we should now be able to convert the amount of BTU that the companies use, to the amount of wattage it releases.

Furthermore, with a given amount of amps, we can also find the amount of power that the air conditioning unit requires to function


Class Discussion - Efficiency of Heat between two blocks.
The next class exercise that we had was to find the the heat and the efficiency of two blocks with similar structures, yet different temperatures (0°C and 100°C respectively), as they reach to equilibrium. It is to note that since this reaction is told to be in a reversible process, finding the average of the heats will not help much in the cause

Finding Heat and efficiency

As it was thought, since we are talking bout a reversible function, ΔS is required. Although the ΔS of the engine is zero, that doesn't mean that the total system is zero, as we had to calculate the two different blocks, which after some calculations turns out to be 46.1°C, which is close to 50°C, the temperature if we were to take the average.
Furthermore, we can find the efficiency of the system by finding the amount of work, since e=W/Qh, turning out to be about 30%

Class Discussion: Horsepower and Stairs:
Another interesting discussion occurs, asking to find the amount of floors per minute a person can climb, by using the notion of horsepower and the amount of meters per floor there are

Measuring the amount of meters per floor

Our calculation in finding the floors per minutes

It turns out that we require to know the potential energy in order to find the amount of energy used during our flight to climb these stairs. Once we found our energy, we needed to find time. Luckily we have the conversion between horse power and watts in order to easily find time, which turns out to be 0.1075 minutes. We then took the inverse of the time (since we are looking for it in terms of 1 floor per minute) in order to find the amount of floors climbed per minute, which turns out to be just over 9 floors per minute.

Class Discussion: Freezing a Popsicle
Our last discussion of the day turned out to be finding out how much time does it take to freeze a Popsicle, knowing the Qc, the amount of mass, and the change in temperature.

Calculations of finding the the time of a frozen popsicle 

Since its in a freezer, we need to know its COP. Once we found that, and understanding that it is 3/4 of a horsepower, we needed to find the amount of wattage it uses. to find the amount of work. Knowing these two units helps us find our Qc, and essentially our Qh as well.

Since this is in a refrigerator, our Qc will help find the time it will take to freeze the Popsicle, understanding our thermodynamics Q=mcΔT, and since we are freezing, that Q=mLf, we can plip the equation to look for time, which turns out to be almost 14 minutes.
It is to note that it will actually take a longer time than 14 minutes to freeze a popsicle in the real world due to the fact that the refrigerator is never on 100% of the time, which can slow down the process to a few hours