Adiabatic Process: Work

[sisigsarap]

I have 5.00 mol of O2(Oxygen) at 20.0 Celsius and 1.00atm. I will compress this to 1/10 the original volume.

Find the work? The correct answer is 46.1 Kj

I am having a terrible time with this.

This is what I know: Q = 0 for an adiabatic process, and the change in internal energy is equal to work.

I think I use integrate Pdv, but I am getting very confused. I am really lost and need a push in the right direction!

 

[faust9]

Ideal gas law? You know pressure, temperature and the number of atoms and 1 atm is much less than the critical pressure.

 

[sisigsarap]

PV = nRT
I just don't see how to plug it in. Pleaseee help its driving me crazy!

 

[faust9]

PV = nRT
I just don't see how to plug it in. Pleaseee help its driving me crazy!

What variable do you not have a value for? There's only one. Solve for the unknown plug in your known values. This will yield your initial condition. Apply the condition in the question. Then use:

$$W=\int_{V1}^{V2}PdV$$

 

[clive]

In an adiabatic process $$Q=0$$ then $$\Delta U+L=0$$ and $$L=-\Delta U$$. You can find now
$$L=-\nu C_V \Delta T$$.
(Because you deal with a diatomic gas, you'll have $$C_V=\frac{5}{2}R$$).

The final temperature is taken from $$TV^{\gamma-1}=const$$ (here $$T$$ is in Kelvin, as you probably know).

OBS. In my opinion, the work made by the gas must be negative!