Isothermal compression of monatomic gas ?

[zaf]

Hello forum members

I need some help on H.W problem...just enough reasoning to atleast get started

the question is as follows:
5 moles of a monoatomic ideal gas at an initial volume of .50 m^3 and an initial pressure of 2.0 * 10^5 Pa undergoes an isothermal compression to .20m^3. Find the final pressure ?

so, the temperature is going to be constant , the inital and final volumes and intial pressure is also know, also the total energy (Q)is going to be work done on the gas... which must be negaive... internal energy is conserved ? am i correct so far...how do i solve this ?

 

[Njorl]

You're overcomplicating. The energy doesn't figure into it. It is also irrelevant that the gas is monatomic. The problem is much easier than you suspect.


Njorl

 

[arcnets]

Right Njorl,
all there is to use is the equation of an ideal gas:
pV = nRT.
Since there is initial & final state, it's a system of 2 equations:
I) p₁V₁ = nRT
II) p₂V₂ = nRT
Now, T is not given, so you better eliminate it:
I) T = p₁V₁/nR
II) T = p₂V₂/nR
Which are clearly equal, so
I = II) p₁V₁/nR = p₂V₂/nR
or (nR cancels)
p₁V₁ = p₂V₂
And we solve for p₂:
p₂= p₁V₁/V₂
OK?

 

[Njorl]

Yes, but I thought it should be left for Zaf to do with just the hint.

Njorl

 

[zaf]

yes. i understand arcnets... thank you

 

[arcnets]

Originally posted by Njorl
Yes, but I thought it should be left for Zaf to do with just the hint.

Njorl

Yes, right. Maybe that was a little too much...