On Monday, we were asked to give a theoretical analysis of a heat engine cycle. This is a picture of the graph we completed with calculated values, given values and other information such as which paths included work being done by the gas or work being done on the gas. The paths in which heat was transferred to the gas and in which heat was transferred from the gas are also noted.
This is the page in our lab book in which I filled in all the necessary values to complete the exercise. The energy at each point on the graph was calculated using the formula E=(3/2)PV since the values of P and V were known at each point. The change in E was found by simply subtracting the internal energy of the initial point of a path from the internal energy of the terminal point of that path. All of the work done either by the gas or on the gas was done at constant pressure, so work could be calculated by W=P(V2-V1). With work and the change in internal energy known for each path, we could determine the heat energy transferred to or from the gas using the first law of thermodynamics. After all this information was found, we calculated the total work to be 1882 J, which is the same value obtained from finding the area underneath the curve.
On Monday, we were also asked to complete some exercises using ActivPhysics. This is a screenshot of Question#6. We noted the initial values of Q and T, ran the simulation until T equaled about 400K, and recorded those final values. We determined the molar heat capacity of a monatomic gas by using the relationship dQ=nCdT and solving for C. We simply inserted our dQ and dT into the equation and found a value very close to that displayed on the screen.
This exercise was very similar to the first, but the simulation was allowed to run for a longer time in hopes of getting a more accurate calculation of molar heat capacity at a constant pressure. Again, we obtained a value of C very close to that displayed in the picture.
In the eighth exercise, we were asked to derive the equation we had been using to calculate the value of C. This is a picture of the derivation, and the final answer of (5/2)R can be seen toward the left. If one plugs in the value of R, 8.314 J/mol*K, into the equation the answer does indeed come out to be 20.8 J/mol*K. I can't say why Andrew decided to draw a flower.
The last thing we did on Monday was to do an analysis of a Carnot engine cycle. However, it was a little different in that the processes of the paths had change. The paths from A to B and from C to D were both isothermal expansions. The path from B to C was an adiabatic expansion, and the path from D to A was an adiabatic compression. Ultimately, we were to determine the thermal efficiency of the Carnot engine by dividing the work done by the engine by the heat that was put in.
We did not finish this in class, so I completed the calculations at home, and they can be seen below. I did not have to use the equation in the upper right hand portion of the paper because I knew that the heat transfer was zero in an adiabatic process. I simply used the first law of thermodynamics to compute the work done since the change in internal energy was easy to compute. The efficiency of the engine came out to be 33.8%, which is about what it should be.
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