A diatomic ideal gas such as air..

In summary, for a diatomic ideal gas such as air with a gamma value of 1.4, expanding adiabatically to 40 times its original volume, the temperature changes by a factor of 1/40 and the pressure changes by a factor of 1/1600.
  • #1
Physics321
12
0
A diatomic ideal gas such as air, for which γ = 1.4, expands adiabatically to 40 times its original volume.
(a) By what factor does the temperature change?
(b) By what factor does the pressure change?

I'm not sure how to attempt/approach this one. If anyone has any suggestions, it would be greatly appreciated.

I tried using the equation T = T(not) - (mgh/R)*(gamma-1/gamma) but I didn't get anywhere, because I'm not sure where the expanding 40 times it's original volume comes in.
 
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  • #2
For adiabatic expansion, there is a simple relationship that involves the initial temperature and initial volume, final temperature and final volume, and gamma.
 
  • #3
Picture1.jpg


Are you talking about this equation? I see it relates pressure, volume, and gamma, but not temperature.
 
  • #4
Physics321 said:
View attachment 23588

Are you talking about this equation? I see it relates pressure, volume, and gamma, but not temperature.

Yeah, there's another one like that, only it relates a product involving T and V before and after the expansion. You could probably derive it from the relation you posted above + the ideal gas law, or you could look it up. It shouldn't be too hard to find.
 
  • #5
So I searched around and found this one. It relates 2 volumes and an initial temperature.

Picture2.jpg
 
  • #6

1. What is a diatomic ideal gas?

A diatomic ideal gas is a type of gas that is made up of two atoms per molecule. Examples of diatomic gases include oxygen (O2), nitrogen (N2), and hydrogen (H2).

2. How does a diatomic ideal gas behave differently from other types of gases?

A diatomic ideal gas follows the ideal gas law, which states that at a constant temperature and pressure, the volume of the gas is directly proportional to the number of moles of gas present. This means that it has a predictable and consistent behavior under certain conditions.

3. What are the properties of a diatomic ideal gas?

The properties of a diatomic ideal gas include having two atoms per molecule, being able to expand and contract easily, and not having any intermolecular forces between its molecules.

4. What are the applications of studying diatomic ideal gases?

Studying diatomic ideal gases is important in fields such as thermodynamics, chemistry, and physics. It helps us understand how gases behave and how they can be used in various processes, such as in engines or refrigeration.

5. Can a diatomic ideal gas deviate from the ideal gas law?

In real-world situations, a diatomic ideal gas can deviate from the ideal gas law at high pressures or low temperatures. This is because at these conditions, the gas molecules are closer together and intermolecular forces start to play a role, affecting the gas's behavior.

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