- #1
thechunk
- 11
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Hey all. I was reading that story about the physics student who is asked to show whether hell is endothermic or exothermic (here's the http://www.people.virginia.edu/~rjh9u/hellthrm.html to the story) when I came upon the following statements:
1. If hell is expanding at a slower rate than the rate at which souls enter hell, then the temperature and pressure in hell will increase until all hell breaks loose.
2. If hell is expanding at a rate faster than the increase of souls in hell, than the temperature and pressure will drop until hell freezes over.
From what I learned in my high school physics class, these are valid statements, however how can one prove the above statements mathematically using the ideal gas laws.
What I have done as of right now, was taking the derivative with respect to time of PV=nRT(nothing is constant except R) to get
<br /> \frac{dP}{dt} V + \frac{dV}{dt} P = \frac{dn}{dt} T R + \frac{dT}{dt} n R<br />
Then I said the system is at STP for convenience with one mol of gas (or souls whatever you want to call them) and got the following
<br /> \frac{dV}{dt} - 22.4 \frac{dn}{dt} = .0821 \frac{dT}{dt} - 22.4 \frac{dP}{dt} <br />
Now assuming that the change in volume as well as the change in number of moles is positive, what conclusions can I make from the above statement. Maybe I took this in the wrong direction or very probably overcomplicated the situation but any help would be much appreciated.
1. If hell is expanding at a slower rate than the rate at which souls enter hell, then the temperature and pressure in hell will increase until all hell breaks loose.
2. If hell is expanding at a rate faster than the increase of souls in hell, than the temperature and pressure will drop until hell freezes over.
From what I learned in my high school physics class, these are valid statements, however how can one prove the above statements mathematically using the ideal gas laws.
What I have done as of right now, was taking the derivative with respect to time of PV=nRT(nothing is constant except R) to get
<br /> \frac{dP}{dt} V + \frac{dV}{dt} P = \frac{dn}{dt} T R + \frac{dT}{dt} n R<br />
Then I said the system is at STP for convenience with one mol of gas (or souls whatever you want to call them) and got the following
<br /> \frac{dV}{dt} - 22.4 \frac{dn}{dt} = .0821 \frac{dT}{dt} - 22.4 \frac{dP}{dt} <br />
Now assuming that the change in volume as well as the change in number of moles is positive, what conclusions can I make from the above statement. Maybe I took this in the wrong direction or very probably overcomplicated the situation but any help would be much appreciated.
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