# Thermodynamics formulas are killing me! HELP

#### Jumb0

5+ Year Member
This is gonna be a big post...so I thank you in advance if you decide to read through the whole thing. I am utterly confused about thermodynamics formulas...I would be forever indebted and appreciative of whoever can help me get these formulas straight:
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• Is the internal energy of a gas U = 3nRT/2 or is it 3RT/2 ? I have seen both formulas and I am confused as to which is the correct one. TBR presents the one that includes the mole term.
• Does it then follow that U = 3PV/2 ?
• And then there's the formula for average kinetic energy of a gas, 3kT/2 . Is this the same as internal energy, U?
• And how about for diatomic gases? I have seen the formula U = 5nRT/2 . Is this correct? Is this useful to know on the MCAT?
• And the first law of thermodynamics says ΔU = Q + W... So U is one of the formulas I gave above, and I know the work done by a gas is supposed to be PΔV, but what is the Q term? Is that the same Q as in Q = mCΔT ?
• Does this mean that the first law of thermodynamics may be written as ΔU = mCΔT + PΔV ?
• And is it the case that heat and work are functions that can only exist when there is change? Indeed, the above formula would suggest that change is inherent to the concepts of heat and work. Is this true? In other words PV is something other than work, and mCT is something other than heat.
• And when the volume of a gas expands, it is said that the gaseous system did work on the surroundings, so the net work of the gaseous system is (-), whereas if the volume of the gas is reduced, that means the surroundings impart work upon the gas, so the work of the gaseous system is (+). But the formula for work of a gas is W = PΔV, so shouldn't a reduction in volume mean a negative change in volume of the gas, and therefore a negative value for work? Perhaps the formula for work is better written as W = -PΔV ?
• So perhaps the first law of thermodynamics ought to written as: ΔU = mCΔT - PΔV ?
• Last but not least, there is this little gem... ΔH = ΔU + ΔPV . Given the other formulas I have presented, would it be fair to rewrite this change in enthalpy as: ΔH = (mCΔT - PΔV) + ΔPV ? But the problem is that the PΔV term implies isobaric conditions, whereas the ΔPV terms implies that pressure is subject to change!

#### texan2414

5+ Year Member
You're not studying for a thermo exam in your P-Chem class...
Besides Q = mcΔT, other formulas you should make aware to yourself are the Gibbs Free Energy, ΔG = ΔH - TΔS; ΔG = -RTlnKeq; know the signficance of ΔG value for spontaneous/non-spontaneous reactions, etc.

#### blackmarble

it depends on how you define the system and the surroundings. i prefer the U = q - W and stick to it so i don't get confused.