Pellet doping

[MSEO1]

Assume you take 6CI of air at room temperature (21C) and normal atmosphere (14psi) and you want to get it to 1000psi. You get:

P1/T1=P2/T2 (The volume of air is constant)
14PSI/21Deg=1000PSI/T2
T2=1500 Degrees.

This ideal gas law treatment isn't quite correct as the volume changes. The amount of air is the same but the volume it occupies is smaller. Work has also been done on the air.

If you look at it as essentially an isentropic process (reversible and adiabatic(no heat transfer in or out)) which means no change in entropy, and use the equation for entropy of a gas:

entropy eqn.png

Since delta S equals zero (no change in entropy) the equation can be rearranged to:

T = T₀e^{(Rln(P/P₀)/C_p)}

Where
T=final temp (degrees Kelvin)
T₀=initial temp (degrees Kelvin) = 21+273=294
R= the gas constant = 8.314 kJ/kmol degC
P=initial pressure (pascals) = 101,325
P₀=final pressure (pascals) = 6,894,747
C_p=specific heat = 29.248 kJ/kmol degC

A quick plug and crank and:

T= 975.7K or 702.7 degrees C

Still pretty hot.

It is also important to use absolute temperatures particularly when taking any ratios and use consistently SI or Imperial units. Hope this helps.

[maecolis]

Heyya MSE01,

You are absolutely correct about your formulas. I'm just keeping it as simple and as quick as I can without a physics lesson... :) But you are right - SI and SAE don't mix... In the case of the ideal gas law, since it's a simple ratio, I felt I could cheat a little.

Note that 700 degrees C is about the temperature you heat treat steel at... and corn oil flashes at about 327 degrees C... :)

Maurice,

Don't worry about the spelling - it's the info that counts. :)

Cheers!