In PV=nRT, since mol of gas,n, is depending on pressure and temperature, how to solve for unknown temperature in the equation?
See Ideal Gas Law Calculator: http://www.webqc.org/ideal_gas_law.html
The background of the problem is the initiation of streamer that leads to what is called partial discharge. I found in an article some conditions that microbubbles should have in order for partial discharge to take place. First, the pressure is 30 MPa. Next, the depth of such microbubble would be around 5-10 micrometer. Since in oil under the influence of electrical field, the form of the microbubble is prolate spheroid, I assumed that polar radius is 20 micron and equatorial radius is 10 micron. Hence, the volume is pretty small. Also due to that, the value of mole should be pretty small also. The data returned a temperature value of unbelievable high. Which I found something is not right somewhere. Or perhaps the ideal Gas Equation interpretation is harder than it seemed.
First, the pressure is too high to assume ideal gas conditions. You should try to use a real gas model instead.
Second point, the ideal gas equation is used to calculate only one variable. From your description, it seems that the number of moles and the temperature are unknowns. If you don't know the number of moles (or the mass) of the bubble, you can't assume it.
Thank you Ahmed Fayez Nassar. By the way, is there any limit of pressure that we can consider as too high for the ideal gas conditions?
Usually we can assume ideal gas conditions up to reduced pressure of 0.1 or 0.2 if the reduced temperature is below 2.0.
If the reduced temperature is higher than 2.0, we can assume ideal gas conditions up to a reduced pressure of about 4.0 or 5.0.
As for pressure of 30MPa, does that mean the pressure within a micro bubble or the bubbles are in the 30MPa environment? In the latter, the pressure in the bubbles may quite different from that outside due to the surface tension.
30 MPa is the pressure inside the bubble as mentioned in ''Watson, P. K., The Growth of Prebreakdown Cavities in Silicone Fluids and the Frequency of the Accompanying Discharge Pulses, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 5 No. 3,June 1998''.
Still wondering how you calculate the temperature simply based on the ideal gas?
Yes, indeed very wrong. I've tried for several numbers of moles based on the volume only and ignoring the effect of pressure and the unknown temperature on the moles itself, which is definitely a wrong assumption. The calculated temperature was too large.
You might try the opposite. Assume a reasonable temperature with the pressure and volume given from the paper, and calculate your mole number see if you get the reasonable mole number. My guessing is that the mole number you plugged in is unreasonably high.
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