What is the volume of the gas after adiabatic compression

[grandpa2390]

Homework Statement

1 liter of ideal diatomic gas (allow for rotation but not vibration) at a pressure of 1 atmosphere and a temperature of 300 K is compressed adiabatically to a pressure of 7 atm. What is the volume of the gas after compression?

Homework Equations

PV=NKT
PV=nRT
$U_T$=f/2*NKT
$PV^gamma$ where gamma=$(2+f)/f$

The Attempt at a Solution

I am not sure how to go about this. I tried just saying 1/7 of a liter, but that is not right. Professor gave a hint about the 5 degrees of freedom being important and not to use 6... I must have missed something... The only formula I have involving the degrees of freedom is the one for the Energy and the PV gamma. but I am not sure how to do that. I thought I would try plugging in the pressure and volume and then changing the Pressure... But I thought I couldn't . Now I am thinking I can again...

 

[grandpa2390]

That's it. I'm sorry. I got blocked because I did not know what PV^gamma was supposed to equal. Then while typing out my question, it dawned on me how stupid I was being. I can just set initial PV^gamma equal to final PV^gamma... I did that and solved for V_final and I got it. It always amazes me how I can sit stumped for hours on a problem. and I'll get it the moment I ask about it. ;)

 

[DrClaude]

That's it. I'm sorry. I got blocked because I did not know what PV^gamma was supposed to equal. Then while typing out my question, it dawned on me how stupid I was being. I can just set initial PV^gamma equal to final PV^gamma... I did that and solved for V_final and I got it. It always amazes me how I can sit stumped for hours on a problem. and I'll get it the moment I ask about it. ;)

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