Adiabatic Expansion of 2.47 mol Ideal Gas: Final Volume Calculation

In summary, an ideal monatomic gas expands adiabatically, has an initial and final temperature of 22.3oC and -64.3oC, and the final volume is 1.52 times the initial volume.
  • #1
espnaddict014
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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.
 
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  • #2
Can You express P through V and T? From ideal gas equation.
 
  • #3
PV = nRT ?
 
  • #4
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
 
  • #5
wait, can you try that again, I don't get what you're saying, sorry.
 
  • #6
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.
 
  • #7
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.
 
  • #8
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?
 
  • #9
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.
 

FAQ: Adiabatic Expansion of 2.47 mol Ideal Gas: Final Volume Calculation

What is adiabatic expansion?

Adiabatic expansion refers to the process in which a gas expands without exchanging heat with its surroundings. This means that the temperature of the gas remains constant during the expansion.

What is the ideal gas law?

The ideal gas law is a mathematical equation that describes the relationship between the pressure, volume, temperature, and number of moles of an ideal gas. It is written as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

How is the final volume of an ideal gas calculated during adiabatic expansion?

The final volume of an ideal gas during adiabatic expansion can be calculated using the equation Vf = Vi (Tf/Ti)^gamma, where Vf is the final volume, Vi is the initial volume, Tf is the final temperature, Ti is the initial temperature, and gamma is the heat capacity ratio of the gas.

Why is adiabatic expansion important?

Adiabatic expansion plays a crucial role in many industrial processes, such as refrigeration and air compression. It also helps in understanding the behavior of gases in various thermodynamic systems, which is essential in fields like chemistry, physics, and engineering.

What factors affect the final volume of an ideal gas during adiabatic expansion?

The final volume of an ideal gas during adiabatic expansion is affected by the initial volume, initial temperature, and the heat capacity ratio of the gas. It also depends on the type of process (reversible or irreversible) and the surroundings in which the expansion occurs.

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