A gas expands from 1L at 1atm to 3L. Assume P is directly proportional to V.
This is a simple question from my second lecture on Thermal Physics, and I have found a way to solve it after my professor made it very confusing in class. My question is more about the formulation of the first law of thermodynamics than this problem in particular. I am confused as to what formulation is valid under what assumptions, rather what assumptions make Eq. 1 (below) valid?
My professor in class stated the first law of thermodynamics as such:
[tex]\Delta E = q + w[/tex] Eq. (1)
Whereas in Baierlein, our course book, it is stated as:
[tex]q = \Delta E + w [/tex] Eq. (2)
The Attempt at a Solution
I have a reference book (Theoretical Physics by George Joos, Dover Edition) that addresses this discrepancy. They present Eq. (1) as one form of the First Law of Thermodynamics under the conditions that all forms of energy are considered to be positive. My thought in this case is that the change in internal energy would not be negative even when the gas expands, and it is up to whomever is using the equation to determine the sign using physical intuition.
Secondly, when they discuss "a change in volume accompanying an external pressure p" they derive Eq. (2) as a special case of the first law, wherein the quantities of the different forms of energy can be either positive or negative. This seems much more intuitive to me.
I believe I was able to solve the problem using the second equation and taking the work done by a gas on its surrounding to be positive (and compression to be negative work), but I cannot see how to solve the problem--or even how exactly to define the problem--if the first formulation of the law is also correct. I have attached a pdf of my solution and the reference book I used. It would be helpful if someone could solve the problem using Eq. (1) and the proper assumptions.