Conceptualizing First Law of Thermodynamics for an adiabatic gaseous system

[markymark71990]

Ok bear with me if this is a little verbose but i am trying to conceptualize these concepts:
For a gas, it is true that energy equals heat plus pressure volume work (1st Law). Thus, for an adiabatic system, any work done on the system by the surroundings will result in an increase in energy (i.e work is positive) Since we know that for the basis of MCAT knowledge P is always constant, and delta V is increasing for the above described adiabatic process in which q is unchanged, the total internal energy must be increasing, which results in an increase in temperature? Is this why gases heat upon compressing? I assume the exact reverse would be true, and thus explains why gases cool upon expansion? Will this always be the case for an adiabatic system?

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[Jepstein30]

I'm having a hard time following exactly what you're asking so I'll run through what I think should answer your questions at some point.

First Law: delta U = q + w
Adiabatic: q = 0

so delta U = w = - P * deltaV

(note the negative in front of that)

I'm confused about what exactly you're saying after that.. it sounds like you're saying you can assume on the MCAT that the external P is always constant? Probably can, unless given information otherwise (and provided the accompanying equation). There's actually a bunch of things you'd have to assume if you want to use the PV equation for work.. but let's just say all of those hold.

delta V is not necessarily increasing though. Two cases obviously:
1) expansion- final volume is greater than initial volume so delta V is net positive, work will therefore be negative as in the gas DOES work on its surroundings
2) compression- final volume is less than initial volume so delta V is net negative, work will therefore be positive as in the surroundings DOES work on the gas

Total internal energy can therefore increase OR decrease..
1) expansion- work is negative so delta U is negative. Internal energy decreases so temperature decreases. Gas will cool.
2) compression - work is positive so delta U is positive. Internal energy increases so temperature increases. Gas will heat.

That is why those two things happen (at least macroscopically, we can also explain it microscopically but who cares).

That's always the case for adiabatic systems and depending on the heat flow (q), it can also be true for other systems. It's always true for adiabatic systems because q is 0 but consider these systems where q = 5 kJ.
1) Gas expands doing 10 kJ of work on its surroundings (-10 kJ). Delta U = 5 kJ - 10 kJ = -5 kJ. Internal energy is decreasing, temperature will drop.
2) Gas expands doing 5 kJ of work on its surroundings (-5 kJ). Delta U = 5 kJ - 5 kJ = 0 kJ. Internal energy is unchanged, temperature will remain constant.
3) Gas expands doing 3 kJ of work on its surroundings (-3 kJ). Delta U = 5 kJ - 3 kJ = 2 kJ. Internal energy is increasing, temperature will rise.

Hopefully that did it.. you're kind of getting on the edge of MCAT-required knowledge though, so don't get too worked up about this (and like I said, because we're working on MCAT assumptions, we're assuming a bunch of things when using these equations.. in reality, it's a lot more complicated for adiabatic expansions).