How Do You Calculate Final Temperatures in an Adiabatically Isolated Cylinder?

[ginger_jj]

Homework Statement

The drawing shows an adiabatically isolated cylinder that is divided initially into two identical parts by an adiabatic partition. Both sides contain one mole of a monatomic ideal gas (), with the initial temperature being 523 K on the left and 287 K on the right. The partition is then allowed to move slowly (i.e. quasi-statically) to the right, until the pressures on each side of the partition are the same. Find the final temperatures on the (a) left and (b) right sides.

http://edugen.wiley.com/edugen/courses/crs1507/art/qb/qu/c15/ch15p_92.gif

Homework Equations

I think that for this kind of problem i need to use W=3/2nRT, however I am not given any of the other variables so i am lost.

The Attempt at a Solution

 

[Doc Al]

adiabatic condition

How do pressure and volume relate during an adiabatic process? Look it up!

 

[m2003]

I would first clarify any uncertainties or missing information in the problem statement. It is important to have all necessary variables and equations before attempting to solve a problem. In this case, the problem does not provide any information about the volume or number of moles of gas on each side of the partition. Without this information, it is not possible to calculate the work done by the gas during the expansion.

Assuming that the volume and number of moles on each side are equal, the work done by the gas can be calculated using the equation W = PΔV, where P is the pressure and ΔV is the change in volume. Since the partition is adiabatic and the temperature remains constant, we can use the ideal gas law (PV = nRT) to find the initial and final volumes on each side of the partition. This will allow us to calculate the work done by the gas during the expansion.

Once we have the work done by the gas, we can use the first law of thermodynamics (ΔU = Q - W) to find the change in internal energy. Since the system is adiabatic, there is no heat transfer (Q = 0), so the change in internal energy is equal to the work done by the gas. Using the equation ΔU = 3/2nRΔT, we can then solve for the change in temperature (ΔT) on each side of the partition.

Finally, we can use the initial temperatures and the change in temperature to find the final temperatures on each side of the partition. The final temperature on the left side will be the initial temperature plus the change in temperature, while the final temperature on the right side will be the initial temperature minus the change in temperature.

In summary, to find the final temperatures on each side of the partition, we need to have information about the volume and number of moles of gas on each side, and we need to use the ideal gas law, first law of thermodynamics, and the equation ΔU = 3/2nRΔT.