- #1

RaulTheUCSCSlug

Gold Member

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## Homework Statement

Assume that in an alternate universe, the laws of physics are very different from ours and that "ideal" gases behave as follows:

(i) At constant temperature, pressure is inversely proportional to the square of the volume.

(ii) At constant pressure, the volume varies directly with the 2/3 power of the temperature.

(iii) At 273.15K and 1.00 atm pressure, 1.00 mole of an ideal gas is found to occupy 22.4 L

Also note that for P and T constant you can assume the volume is proportional to the number of moles of gas.

## Homework Equations

PV=nRT

P∝1/V^2 for constant T

V∝T^2/3 for constant P

V∝n for constant P and T

## The Attempt at a Solution

Okay so I understand that when the ideal gas law was derived, each variable was held constant, then seen how the other variables changed and was related through a proportionality constant R. I also know that for the original ideal gas law, PV was proportional to T and PV is proportional to mT so therefore when you add the constant of proportionality R, the relation is clear that PV=nRT.

But for the instances given I can only get that since P is proportional to 1/V^2 and V is proportional to n, then it would make since that in the final solution it is something like P/V^2=Rn^2T^2/3 in which R is constant. But that is not what the solution states.

Solutions answer is PV^2=n^2RT^4/3.

Why is the T^2/3 squared...? Is it because the Volume is squared? Thus both N and T have to be squared? And how does this show that P is proportional to inverse V squared. I'm just really stumped and I don't think I understand the concept of holding a variable constant or something...