A sample of 20.0 moles of a monatomic ideal gas (γ = 1.67) undergoes an adiabatic process. The initial pressure is 400kPa and the initial temperature is 450K. The final temperature of the gas is 320K. What is the final volume of the gas? Let the ideal-gas constant R = 8.314 J/(mol • K).

Question

aaronq · Answer

$$\frac{ T _{2} }{ T _{1} }=\left( \frac{ V _{1} }{ V _{2} } \right)^{\gamma-1}$$

you can find the derivation of this in your book, or the internet (google "adiabatic compression")

aaronq · Answer

ps find the initial volume first

anonymous · Answer

I did:
PV = nRT
P = 400 kPa
n = 20.0
T = 450 K
V = nRT/P = 20 * 8.314 * 450 / 400 = 187 L

V1/T1 = V2/T2 and I'm solving for V2
V2 = V1 (T2/T1) = 187 x 320 / 450 = 133 L

My answer doesn't match the choices. I don't know what I did wrong.):

the choices are: 
A. 230 L
B. 350 L
C. 270 L
D. 190 L
E. 310 L

aaronq · Answer

you didn't take into account the exponent, gamma-1 on the (V1/V2)

anonymous · Answer

Does gamma-1= -0.422784?

anonymous · Answer

Is this gamma the same thing as euler's constant?

aaronq · Answer

nope, gamma (the heat capacity ratio) was given in the question. http://en.wikipedia.org/wiki/Heat_capacity_ratio

anonymous · Answer

Ohhh, I didn't even notice the 1.67. 

Thank you for your help!

aaronq · Answer

no problem! read the question next time :P