A simple thermoelectric generator with two water reservoirs.
We add hot water and cold water to either side of the setup/
As the heat is transferred, some energy is being extracted from the exchange and converted into electrical energy; which, in turn, powers the motor spinning the wheel.
Hooking up an electric current to the device reverses the process and allows heat the flow backward from cold to hot.
The device being powered and a brave soul attempting to feel the effects.
Written observations of the device in effect. We describe our predicted and observed outcomes from each process.
We equate and solve for the molar heat capacity of gasses, and found a direct relationship with the ideal gas constant. This calculation was done under the assumption of constant volume.
Under constant pressure, we solved for the constant again but found a different value due to work being done on the system.
We substitute the values we just found back into the ideal gas law formula for an adiabatic process to verify that two molar heat capacities' difference just equals the ideal gas law constant.
If the change in internal energy is equal to the negative work done, we can equate two formula and solve for a constant n\DeltaT
And equating the two equations and some algebra, we have an equation that can be easily integrated after we substitute the \Deltas with differentials.
Integrating shows that the natural log of initial over final are different by a factor for Cp / Cv. We can then move the constant up as an exponent and take exponential of both sides.
We substitute the new equation we just derived back into the ideal gas law and find an equation relating the temperature and volume for adiabatic processes.
Of course, the last step is to integrate the equation to find the work done by an adiabatic process. There is actually an error in this picture since we plugged in the initial and final values incorrectly.
After fixing the equation, we then solved a example problem given based on what we had just derived.
Since we can now find the work done by an adiabatic process, we went back to engine problems, this is the given data for out problem.. We used our isotermal methods along with the new formulas we derived to find work and heat added or lost.
Since the ideal gas law says that PV = nRT, we can substitute for P in the work integral, finding a forumla for work done without the need for calculating pressure.
One of the formulas we derived for the adiabatic processes relating two points in the cycle. The pressure-volume diagram is also shown in this picture. The values were calculated from the formulas derived from the ideal gas law.
The final results of the calculations, we found information for every point on the graph as well as the changes in internal energy in the heat and work component form.
A model of a Carnot engine.
The piston does work since the gas expands and pushes it down.
A light shows when the spark ignites the gas.
Ways that we can improve on engines.
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