How many degreed of freedom have the gas molecules,if under standard conditions the gas dendity is 1.3kg/m^3 and velocity of sound propagation on it is v=330m/s?
<v> =sqrt{3RT/M}=sqrt{3pV/m} =>
M=mRT/pV =ρRT/p.
v=sqrt {γRT/M}.
γ=C_p /C_v = (i+2)/i.
v=sqrt{9i+2)RT/iM} = sqrt{(i+2)RTp/iρRT}=
=sqrt{(i+2)p/iρ},
iρv² - ip = 2p,
i=2p/ (ρv² - p) =
=2• 1.01325• 10⁵/(1.3•330²-1.01325• 10⁵)
=4.9 ≈ 5.
i=5
What is the value at NTP
To determine the degrees of freedom of gas molecules under standard conditions, we need to consider the kinetic theory of gases. According to this theory, each molecule in a gas can move independently in three dimensions: x, y, and z. Therefore, each molecule has three degrees of freedom associated with its translational motion.
However, for diatomic molecules (such as oxygen or nitrogen), we also need to consider rotational motion. Each diatomic molecule can rotate around two axes, adding two additional degrees of freedom. So, for diatomic gases, the total count of degrees of freedom is five.
To calculate the degrees of freedom for the gas in question, we need to know its molecular composition. If it is a monatomic gas (such as helium or argon), then we only consider translational motion. In this case, the gas has three degrees of freedom.
Since the question does not provide information about the molecular composition, let's assume it is a monatomic gas. Thus, we can conclude that the gas molecules under standard conditions have three degrees of freedom.
The given information, such as gas density and velocity of sound propagation, doesn't directly provide us with the number of degrees of freedom. Instead, it helps us understand the behavior and properties of the gas.