How Is the Joule-Thomson Coefficient Calculated Without Knowing Volume?

[alexandria7]

Hi. I need a little help with this question. I found a useful link below but can't figure out how to find the joule-thomson coefficient without knowing volume. I'd appreciate any pointers on this. Thanks.

http://www.ccr.buffalo.edu/etomica/app/modules/sites/JouleThomson/Background3.html

Steam at 12 MPa and 450 oC is throttled in a valve to a pressure of 5 MPa in a steady flow process. Determine:

-the new temperature of the steam
-the entropy generation for the process and check if the second law is satisfied

Steam table:

P (Mpa) T (oC) h (kJ kg-1) s (J g-1 K-1)
12.0 450.00 3209.8 6.3028
5.0 350.00 3069.3 6.4516
5.0 360.00 3095.6 6.4935
5.0 370.00 3121.5 6.5340
5.0 380.00 3146.9 6.5732
5.0 390.00 3171.9 6.6112
5.0 400.00 3196.7 6.6483
5.0 410.00 3221.2 6.6844
5.0 420.00 3245.4 6.7196

 

[Astronuc]

One can use specific volume, which one can look up in the appropriate table, as one has found specific enthaply and specific entropy.

 

[piercas]

5.0 430.00 3269.3 6.7539
5.0 440.00 3292.9 6.7875
5.0 450.00 3316.3 6.8202

The Joule-Thomson coefficient can be calculated using the following equation:

μ_JT = (T(2) - T(1))/(P(2) - P(1))

Where T(2) and T(1) are the temperatures at the final and initial pressures, respectively, and P(2) and P(1) are the final and initial pressures, respectively.

In this case, we know that the initial pressure is 12 MPa and the final pressure is 5 MPa. We also know that the initial temperature is 450 oC, but we do not know the final temperature. In order to find the final temperature, we can use the steam table to interpolate between the two temperatures at the given pressures. From the table, we can see that at 5 MPa, the temperature ranges from 350 oC to 450 oC. We can choose a temperature between these two values, say 400 oC, and use it to calculate the Joule-Thomson coefficient. This will give us an approximation of the final temperature, and we can repeat the process with a different temperature until we get a more accurate value.

Once we have the final temperature, we can calculate the Joule-Thomson coefficient using the equation above. This coefficient represents the change in temperature for a given change in pressure, and it is a measure of the cooling or heating effect of the throttling process.

As for the entropy generation, we can use the following equation:

ΔS = m*(s(2) - s(1))

Where m is the mass flow rate and s(2) and s(1) are the specific entropies at the final and initial states, respectively. This equation represents the change in entropy during the process, and it can be used to check if the second law of thermodynamics is satisfied. If the value of ΔS is positive, it means that there is an increase in entropy, which is in line with the second law. If the value is negative, it means that there is a decrease in entropy, which violates the second law.

In order to find the mass flow rate