Entropy and Cycles

We started the day comparing the two different cycles, auto cycle and diesel cycle. The difference between them is that diesel cycle expands Adiabatic until gas ignites, which makes the pressure constant in the end. It also compresses gas further. Thus, it makes it more efficient, but the max Power is lower because it goes through more cycle?

We now learned about entropy. Entropy is heat divided by temperature. When the situation is adiabatic, entropy becomes what it's called as isoentrophic.  

We then learn briefly about stirling engine. 

It is known to be ecofriendly. There are 4 steps in stirling engine; expansion, transfer, contraction, and transfer. This is called Brayton cycle. From this cycle, we draw the relationship between the pressure and entropy. The shape of the graph becomes parallelogram. We have learned about first law of thermodynamics in the past lecture. Today, we are learning about the second law of thermodynamics, which says energy can be created, but not spontaneously destroyed.

Using this definition, when put into a graph of temperature vs entropy, adiabatic becomes vertical line, and isothermic becomes horizontal line. Whereas Isovolumetric becomes the graph of adiabatic, and isobaric becomes the graph of isothermic on first law.

Stirling engine works with different temperatures, just the same as thermoelectric cooler. The difference is we will be putting a cold temperature on top of the engine, and hot on the bottom to create energy that can move the propeller. The location of hot and cold can also be switched, and it will cause the propeller to spin the other way. 

We learned some new equations about coefficient of ? To find the heat ? First, we wanna find its max coefficient by dividing the temperature of a system with temp of system minus temperature of outside. Using that max coefficient, we can find the heat by multiplying it with the power given as below.

Given a different problem, we find the work the same way as we did just now, except we divide the heat by the max coefficient. We find each work that the system gives out and also the actual work needed. Finding that, we can then calculate the efficiency by dividing the works and multiply them by 100%.

We knew from earlier that heat inside is sum of heat outside and work of the system. Change in entropy of a sytem is zero. Using that, we find the sum of entrphys of a system to find final temperature. Since heat is mc*delta T, we can integrate change in entropy and temperature, and find the equation to be mc*ln(Tf/Ta). Adding the two temperatures, we can put them together in to mc*ln(Tf(square)/Ta*Tb). Now we can solve for final temperature as below.

After finding the final temperature, we can now find the work by subtracting heat in by heat out.