Speed of sound in an ideal gas

[greg_rack]

Homework Statement

2.0kg of an ideal monoatomic gas(γ = 5/3) are contained inside a box of volume V=4.2m³.
Gas is at a pressure of 3.5bar.

-Calculate sound's velocity through the gas

Relevant Equations

Speed of sound in a gas: ν=√(γkT/m)
IGE: pV=nRT

First of all I thought it was necessary to calculate the temperature(the only data missing for the formula) using the ideal gas equation(since I've already been given 'p' and 'V'), and plug it in the 'v' formula, but the problem immediately occurred when i tried to find out the number of moles(n), that I couldn't manage to find... and that's exactly where I got stuck.

 

[gneill]

"monoatomic gas" means that your gas is composed of only one atom, or $n=1$.

That is incorrect. Here n represents the number of moles of the gas present.

There is another formula for the speed of sound in a gas that involves pressure and density. Take a look at the wikipedia article on Speed of Sound.

 

[archaic]

That is incorrect. Here n represents the number of moles of the gas present.

There is another formula for the speed of sound in a gas that involves pressure and density. Take a look at the wikipedia article on Speed of Sound.

Yes, I have deleted that comment, but somehow you were faster

 

[greg_rack]

That is incorrect. Here n represents the number of moles of the gas present.

There is another formula for the speed of sound in a gas that involves pressure and density. Take a look at the wikipedia article on Speed of Sound.

Yeah, you're definitely right... I managed to solve the problem using the wikipedia formula "v = √(γ *p/d)", but I cannot understand why this works since in my physics book the only formula explained is "v = √(γ*k*T/m)", from which i cannot derive the resolving one!

 

[gneill]

That wikipedia page shows the relationships:

More detail can be found on the Hyperhysics web page for the speed of sound in gases.

 

[greg_rack]

That wikipedia page shows the relationships:

View attachment 256246

More detail can be found on the Hyperhysics web page for the speed of sound in gases.

Thank you so so much... I just found out that Italian wikipedia isn't that clear at all!
Thanks again

 

[gneill]

You're welcome!