Adiabatic Expansion of 2.47 mol Ideal Gas: Final Volume Calculation

[espnaddict014]

An ideal monatomic gas, consisting of 2.47 mol of volume 0.0890 m^3, expands adiabatically. The initial and final temperatures are 22.3oC and -64.3oC. What is the final volume of the gas

According to a formula in the book, the volume of an ideal monatomic gas' volume expands by 1.52, but I think I am misinterpreting that. Anyway, I have tried using the formula

V2/ V1 = (P1/P2)^y -- but I don't know how to get the second pressure. Any help would be appreciated.

 

[Yegor]

Can You express P through V and T? From ideal gas equation.

 

[espnaddict014]

PV = nRT ?

 

[Yegor]

Yes. You know that P*V^(gamma) is constant!? So P1*V1^gamma=P2*V2^gamma
But V=V(P,T). Thus, You can find any function depndent on V and T which is constant. it will be like V*T^(q), where q is any coefficient which can be expressed with gamma

 

[espnaddict014]

wait, can you try that again, I don't get what you're saying, sorry.

 

[Yegor]

You have PV = nRT. n and R are constant.
You also know V2/ V1 = (P1/P2)^y (do You understand what is y?)
From other angle P1/P2 = (T1*V2)/(T2*V1) (From ideal gas equation), isn't it?
So, know You can express T1/T2 through V1/V2.

 

[espnaddict014]

No, I don't understand y
It says that y = Cp/Cv -- and then it lists values for real gasses, but this is a general gas

I see what you're saying for the second part, I guess I just am frustrated with looking at it.

 

[Yegor]

As You have written "V2/ V1 = (P1/P2)^y", y =Cv/Cp. Usually is used gamma = Cp/Cv=1/y. did You get the answer?

 

[espnaddict014]

Yeah, its gamma, I just don't know how to put gamma on the computer. Anyway, no, I am still very confused. Don't worry about it, I'll try to solve it, I guess I just don't know where to get started with all of these formulas. Thanks for the help though.