Isothermal Expansion of a Diatomic Gas

[MaryCate22]

Homework Statement

A 0.300-kg sample of nitrogen gas (diatomic molecules,mN2 = 4.652 × 10^−26 kg) in a chamber fitted with a piston undergoes an isothermal expansion from 0.0500 m^3 to 0.150 m^3 .

If the final pressure is 110 kPa, what is the final temperature?

Homework Equations

PV=N*kB*T where Boltzmann's Constant is kB=1.38*10^-23 J/K

The Attempt at a Solution

Because the process is isothermal, PV = constant and Ti = Tf.
To use the formula, I need N (number of molecules).

0.300/[(4.652*10^-26)(0.5)]=1.29*10^25

Plugging this N into T=PV/NkB I get, T = 92.7 K, which is not the right answer.

I don't think diatomic gasses behave ideally, but I have no idea how to reflect that in the formula. I also do not know how the initial volume and pressures are relevant.

 

[MaryCate22]

The question is what is the final temperature if the final pressure is 110 kPa. Sorry, I'll edit.

 

[MaryCate22]

Just a thought, am I supposed to use the number of molecules or the number of atoms?

 

[Bystander]

,mN2 = 4.652 × 10^−26 kg

0.300/[(4.652*10^-26)(0.5)]=

am I supposed to use the number of molecules or the number of atoms?

 

[MaryCate22]

Well that clears it up. Thank you.

 

[lep11]

N is the number of particles which can be molecules, atoms, ions etc.