# Thermo: ideal gas problem

An unknown number of Helium atoms are in a 1 liter container at an unknown temperature. The gas is made to expand such that it's final volume is 4 liters and pressure rises 'in direct proportion to its volume'.

1. does 'in direct proportion to it volume' mean Pf = Pi * Vf/Vi or should there be a proportionality constant a?

2. I calculated the work done on the gas by using P(v) = a*V and using W = -[inte] aVdV = -a/2 * (Vf^2 - Vi^2) Comments?

3. I am having more trouble getting change in internal energy dU.

I tried PV = NkT so PfVf - PiVi = Nk( Tf - Ti) and
dU = 3Nk (Tf - Ti)/2 so that

dU = 3/2 * (PfVf-PiVi) = 3/2 * (4*4*aVi - Vi)

Is this even close?

4. If I can get 2 and 3 I can calculate Q myself!

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HallsofIvy
Homework Helper
"Pressure is in direct proportion to Volume" MEANS that P is some constant times V: P= aV where a is the constant of proportionality.

HOWEVER, if you write P1= aV1 and P2= aV2 for two different sets of pressure and volume, and then divide one by the other: P1/P2= V1/V2 (which is the equation you are using) does not involve a constant of proportionality because they cancel.

2) looks correct to me.

In 3) You use PV= NRT which says that for CONSTANT temperature, P is INVERSELY proportional to V. But the problem says P is directly proportional to V! Well, of course, that says that the temperature does NOT stay constant! You can use PV= NRT together with P= aV to find the change in temperature just as you did.