# Physics Question?

I know that this is not a project related question and I promise not to make it a habit, but my physics teacher stumped our class with a question today and I thought of all the smart people on Instructables one of you would know the answer. I have already search google to no avial. Is it possible to determine the volume of a flask given only the starting temperature/pressure and the final temperature/pressure? The number of moles are unknown. If it is possible how do you determine it? Thanks for your help!

active| newest | oldestyou will use the law of Avogadros!

Avogadro's law (sometimes referred to as Avogadro's hypothesis or Avogadro's principle) is a gas law which states that, under the same condition of temperature and pressure, equal volumes of all gases contain the same number of molecules. The law is named after Amedeo Avogadro who, in 1811,[1] hypothesized that two given samples of an ideal gas, of the same volume and at the same temperature and pressure, contain the same number of molecules. Thus, the number of molecules or atoms in a specific volume of ideal gas is independent of their size or the molar mass of the gas. As an example, equal volumes of molecular hydrogen and nitrogen contain the same number of molecules when they are at the same temperature and pressure, and observe ideal gas behavior. In practice, real gases show small deviations from the ideal behavior and the law holds only approximately, but is still a useful approximation for scientists.

Avogadro's law is stated mathematically as:

V/n=kWhere:V is the volume of the gas. n is the amount of substance of the gas.

k is a proportionality constant.

The most significant consequence of Avogadro's law is that the ideal gas constant has the same value for all gases.

This means that:

p1V1/T1n1=p2V2/T2n2=constant!Where:p is the pressure of the gas in the cell

T is the temperature in kelvin of the gas

see the second formula!

Since both the volume and quantity of gas are unknown, you need two equations to solve for both of them. You're given two different (T,P) values, so you can write down two equations, one for (T0,P0) and one for (T1,P1). Now you can solve them for V and n, and just don't bother evaluating n :-)

If you don't know how to solve a set of simultaneous equations (you would have learned it in your linear algebra course), that's okay. Once you've gotten the two equations above, come back here and post them, and we can walk you through the rest of the process.

V/n = RT1/P1 = k (k from V/n = k)

P1(nk)=nRT1 -> P1k = RT1 (which does not seem to help at all)

P1V=nRT1 -> V/n = RT1/P1

P2V=nRT2 -> V/n = RT2/P2

V and n are unknown, but are constant throughout.

I mean supposing I've got this flask. Also the flask closed so that its internal volume V and the number of moles n of gas inside are both constant. Also the flask has two sensors attached to it. A thermometer measures T and an pressure gauge measures P.

Starting with the ideal gas law: P*V = n*R*T

I divide both sides by V. Then group together all the constant terms in parentheses, to get:

P = (n*R/V)*TNow a plot of P as a function of T should be a straight line that intersects the origin (T=0,P=0) and has a slope of (n*R/V). With two or more good data points, you know, measurements for (T,P) I should be able to find the slope of that line.

But then what?

How do I decompose (n*R/V) = constant, without knowing either n or V?(Presumably I can look up R in the back of the book.)Of course, if this were a real flask in my laboratory, I could just use a tape measure to measure its outside dimensions, and estimate its internal volume. Or maybe I could fill it with jelly beans (of known density) or something like that. But tricks like these I could perform without the ideal gas law.

just one good data point, since:(P/T) = (n*R/V) = constant