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relativespeak

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## Homework Statement

Imagine some helium in a cylinder with an initial volume of 1 litre and an initial pressure of 1 atm. Somehow,

the helium is made to expand to a ﬁnal volume of 3 litres, in such a way that its pressure rises in direct

proportion to its volume.

(b) Calculate the work done on the gas during this process, assuming that the process occurs quasi-statically,

and no other types of work are being done.

(c) Calculate the change in the internal energy of the helium during the process.

(d) Calculate the amount of heat added to or removed from the helium during this process,

(e) What would you have to do to cause the pressure to rise as the helium expands?

(f ) Describe a simple experimental setup in which this form of the expansion would occur, i.e., where the

pressure would rise proportional to the volume of the gas.

## Homework Equations

W = -∫PdV

U = Q+W = (f/2)NkT

PV = NkT

## The Attempt at a Solution

For the first part I used W = -∫PdV and P=mV where m is some proportionality constant. Then W=-∫mVdV= -(m/2)V^2 which equals -m*4E-6. I'm not sure if this work is correct.

Then for part c, U=(3/2)NkT=(3/2)PV=-(3/2)W (because helium has 3 degrees of freedom) and the heat is given by:

-(3/2)W=Q+W, Q=-(5/2)W. I'm just not sure if this is correct

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