We asked ourselves: "what would happen to a flame inside a sealed bottle if the bottle was free falling?"
In my group we answered that the flame would get dimer because gravity would be pulling down on the bottle. But although we got the right answer, it was actually due to the distortion of the convection currents. This happens because the flame heats the air on top of it and makes that air push onto other air so that it goes down to feed the flame. However, these air currents become disrupted as the bottle enters free fall and all of the gas particles start moving in different directions.
Next, we were asked to come up with a system that would store energy. My group came up with the example of compressing a spring.
The thought was that we put energy into the spring when we compress it. Then we keep it there and release it when we need the energy back. Hence, the energy was stored.
These exercises got our minds thinking about thermodynamic processes, so we answered some questions from a software about state variables and the ideal gas law during different processes.
The first question was to identify the shape of a graph that would depict the volume-temperature relationship during an isobaric processes. Our group correctly answered using the ideal gas law that they are proportional to each other and their graph would look linear.
The second question was asking the same about the pressure-temperature relationship during an isochoric process. And, again my group correctly answered using the ideal gas law that they are proportional to each other and that their graph would look linear as well.
The third question was different. It asked about the pressure-temperature relationship during an isothermal process. Using the ideal gas law, we identified the shape of the graph to be that of an inverse equation. And, we found that pressure and temperature are inversely related to each other. Our work is on the left side of the picture below.
The fourth question was to actually calculate something, but, now that we were professionals at working with the ideal gas law, this was a piece of cake. The question was to calculate the volume after an isobaric process. Since n, R, and P are the same, we came up with an equation that allowed us to not have to convert units and maintain the ideal gas assumptions. Our work is on the right side of the above picture.
The fifth question was to calculate something as well. We were asked to calculate the pressure in a system after an isochoric process. Since it is an isochoric process and there is change in molecules, we can say that n, R, and V are constant and came up with an expression that allowed us to easily calculate the pressure given the initial conditions. Our work is on the left side of the picture below.
The sixth question was to calculate pressure once after it has gone through an isothermal process and then once again after it has gone through another isothermal process. Again, there was no change in the count of molecules. So we came up with an expression that, since both process are isothermal, allowed us to use it for both cases. Our work is on the right side of the picture above. It was mislabeled Question 4 but it is actually Question 6.
Then we identified what it means when a pressure vs volume graph looks a certain way. Each of the graphs below corresponded to one of the four thermodynamic processes that we studied so far: isobaric, isochoric, adiabatic and isothermal.
My group correctly identified each graph corresponding to the correct process. Nevertheless, we struggled when it came to the last two, and the reason was how to differentiate between adiabatic and isothermal processes when they look so familiar and have similar mathematical relationships. The answer was to look at the actual mathematical equation and see that, for adiabatic processes, there volume is raised to a power. This makes its graph look much steeper.
Happily, we got the right answer.
Then we solved a problem that was going to help us solve the next problem. It involved calculating the energy it takes to lift about 38 m^3 of water 40 m into the air into a sealed tank. We weren't sure how to solve it at first, but Prof. Mason patiently guided us. It required us to calculate three things. First, there is work being done in lifting that volume of water into the tank. Then, there is work done in compressing the air inside the tank. And finally there is work done by the air outside that helps pump the water into the tank.
So we calculated the work being done by the pump into lifting the water with the change in potential energy. We had to remember that the tank was getting filled only 3/4s full. This is necessary to calculate the amount of water that is being transported and the energy required to lift it. Then, the work that is done on the air occurs at constant temperature, so it is an isothermal process. Therefore, the work done on it is calculated by using a differential volume and integral. And, the work of the air that helped the pump lift the water. All these are in one equation that finds the net work.
Next, we calculated the work involved in the movement of a frictionless syringe. This syringe was moved slowly so that there was no change in internal energy.
Then we came up with the processes that make a rubber band work as a part of machines that transports goods. Below there is a picture that says what these processes are as part of the cycle.
From the regular equation for efficiency, another formula was calculated to be used. This new form is a little easier to use than the original one.
Then we studied a cycle that was composed of two isobaric and two isochoric processes. The isobaric processes are the horizontal lines and the isochoric processes are the vertical lines. We deduced that, since pressure is constant and volume is changing, the temperature must be going up and so heat is coming in when there is an expansion. Also, expansion means that there is work being done by the system. Then, pressure decreases while the volume stays the same, so temperature must be decreasing as well. Hence, heat is coming out of the system. Then, the pressure is constant while there is a compression, so temperature is decreasing. Hence, heat is going out of the system. There is work being done onto the system. The last process has the volume constant while the pressure increases, so heat must be coming in. This is a cycle since all the processes are repeated in the same fashion.
Below are shown the quantities that we had to calculate to find the efficiency of the system. They are in the order that they had to be calculated in order to find everything about the thermodynamic cycle.
Below are the calculations that were done in class. These involved calculating the change in internal energy of the system, the work done during each process, the heat involved, the overall work, heat and change in energy and the efficiency of the cycle.
Summary
Today we studied four thermodynamic processes. These are adiabatic, isothermal, isobaric, and isochoric. These were solving problems on the computer, understanding a real life problem (filling a tank), and solved cycles that involved some of them.
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