Today we observed heat flow making a spinner spin. The right reservoir was full of hot water and the left reservoir was full of cold water. We called the hot water the hot reservoir and the cold water the cold reservoir. Unfortunately, our hot reservoir was not providing enough heat flow, so instead we used a mini flame thrower as the heat source.
The heat made the spin spin really fast as shown in the picture below. Our observations were the following: one side was really hot, and the other side was really cold. After the spinner was spinning for a while, the cold side was getting hotter. This means that there was heat transfer involved.
Afterwards, we cooled both sides and the spinning stopped. Then, we connected the spinner to an electricity source and spin began spinning. Nevertheless, it also warmed one of the sides up and cooled the other.
This means that the machine works by providing a difference of temperature or by providing electricity.
This is an example of a reversible thermodynamic process. Also, there is a relationship between heat and electricity that is going on in this apparatus. Prof. Mason said that the material the machine was made out from was designed to the nano level so that when it gets hot, the molecules vibrate in a specific way and make an electron flow which makes electricity and feeds the motor and spins the spinner.
Next we tried to analyze a heat engine that could lift a small mass.
First, we calculated the volume of air that would be sealed inside the engine and then identified the processes that were happening while the syringe was lifting the mass.
We managed to do that, but unfortunately, our machine wasn't working very well, so we decided to change the syringe. The new syringe seemed like it was going to work better because it was frictionless and seemed to work a lot smoother.
We recorded data on Logger Pro and tried to calculate the work done by the system and ended up with the graph and points below.
The work done by the system during the entire cycle is depicted by the shaded area which means that this was basically a geometry problem by then.
We divided our shape into parts whose area was easier to calculate. Then, we found out how to calculate the work of the overall system by hand. We ended up having to calculate the areas of trapezoids, rectangles and triangles.
These are the conditions at each of the four steps. We wrote them down as the cycle was running.
Next we wanted to derive the relationship between R and cp through the first law of thermodynamics. It turned out that R and cp are relating.
We did the same for cv and R, and found out that R and cv are also related.
Next we worked with the formulas some more. We developed a formula that can help us solve for the details of an adiabatic process.
The final equation has deltas. When they are replaced by element differentials and integrated, we obtain the formula in the picture below right after the ideal gas law equations.
Using the ideal gas law, we transformed this equation to make a relationship between temperature and volume during an adiabatic process.
Then, we used this formula to develop our equation for work during an adiabatic process.
Then we used this formula to calculate the work during the adiabatic process in our small heat engine.
Then we used our formula to solve for all the details of a simple Carnot Cycle. First we wrote down the pressure, volume and temperature. Then, we calculated the change in energy, work and heat for each process. And, then we calculated the net change in energy, work and heat. Finally, we calculated the efficiency.
Below is a model of a gasoline tank inside a car. The model shows a thermodynamic cycle and allowed us to visualize how these processes actually takes place.
Summary
Today we worked through thermodynamic cycles. Also, we worked through a lot of equations to find easier formulas to work with and learn about new relationships between constants. We also observed a model to help us see the cycle from a physical point of view.
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