Free (mostly) Expansion of an Ideal Gas

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SUMMARY

The discussion centers on calculating the gauge pressure of air in an insulated container with a known volume and orifice size as it is heated. The initial conditions are set at 300K and 1 atm, with a container volume of 0.0033 m3 and a circular orifice area of 9.0E-6 m2. The heating rate is specified as 1°C/min. The user, slader99, utilized the ideal gas law and Bernoulli's equation to estimate the gauge pressure, arriving at a value of approximately 2.4E-6 mbar, while expressing discomfort with the assumptions made during the analysis.

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Slader99
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Hey All,

Had a problem to solve and wanted to know how others would approach it. Problem is as follows:

An insulated container of known volume has an orifice of know size. Container is filled with air and left to rest so that temperature and pressure is that of atmospheric surroundings. Container air is heated at a know rate which causes mass flow through orifice. What is the container pressure (gauge) resulting from the heating of said air?

Givens:
1) Initial temp is 300K and initial pressure 1atm.
2) Volume of container is 0.0033m^3
3) Orifice is circular of area 9.0E-6 m^2
4) Rate of temperature change is 1C/min

If you were to craft a formula for pressure as a function of rate of temperature change what would it look like? If you were to solve for pressure based on the givens above what would you get for Pgauge?

When I did the exercise I had to make more assumptions than I’m comfortable with. I ended up using the ideal gas & Bernoulli equation to arrive at a value in the range of 2.4E-6 mbar.


Thanks!
slader99
 
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