For the following question I was able to find the heat transfer and the entropy but I am having trouble finding the work done. When i solved delta E = Qnet - Wnet I got Win = Wout but Im not sure that is correct. I think that i need to solve for the final temp and pressure but again I am stuck there. P1V1/T=P2V2/T2 wont work and since it is air and not an ideal gas PV=RT won't work either. Does anone have an idea?
3.1 One kilogram of air in a piston-cylinder device undegoes a thermodynamic cycle composed of the following reversible processes: 1�¨2 air at 2.4 bar and 250 K is expanded
isothermally to 1.2 bar; 2�¨3 air is then compressed adiabatically back to its initial volume; 3�¨1 air is finally cooled at constant volume back to its initial state. Account for variable
specific heats.
c) Calculated the work, heat transfer, and entropy change for process 2�¨3 (57.3, 0, 0)
I don't understand the meaning of "2 air, "1 air, "3 air etc
You should be able to treat air as a perfect gas, even if the specific heat is not constant.
The work done will be the sum of the integral of P dV for steps 1 and 2. Use the gas law to make P a function of V.
For the cycle, Qin - Qout = Wout
those should be arrows. I think when i used the cut and paste function it messed up!
No problem! I'll help you figure out the work done for process 2 to 3 in the given thermodynamic cycle.
In this case, "2 air", "1 air", and "3 air" are referring to the different states of air in the cycle.
To calculate the work done, we need to find the integral of pressure (P) with respect to volume (V) for the process 2 to 3.
Step 1: Express pressure as a function of volume. Since we are treating air as a perfect gas, we can use the ideal gas law to relate pressure, volume, and temperature.
The ideal gas law is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Step 2: Determine the relationship between pressure and volume for the given process 2 to 3. If you have the specific values for initial and final states, you can calculate the temperatures for each state using the given information. Make sure to use the variable specific heats of air since they were mentioned.
Step 3: Once you have the pressure-volume relationship, you can integrate the expression PdV over the volume range from the initial volume to the final volume to find the work done during this process.
Step 4: Finally, use the equation ΔE = Qnet - Wnet to find the work done. In this case, the heat transfer (Qnet) for process 2 to 3 is given as 0, so ΔE = -Wnet.
To summarize, you need to determine the pressure-volume relationship for process 2 to 3 using the ideal gas law, and then integrate PdV over the volume range for this process. This will give you the work done in this step of the cycle. Make sure to consider the variable specific heats of air in your calculations.