Basis of degree of freedom for monoatomic and diatomic mixture

[nomorevishnu]

hi guys

16 grams of helium gas is mixed with 16 grams of oxygen...
what will be the ratio Cp/Cv of the mixture...

how to calculate it?? i thought on the basis of degree of freedom for monoatomic and diatomic mixture...but that can take me to the answer only by approximation...how do we arrive in a a formula that could get me answer...

 

[Andrew Mason]

16 grams of helium gas is mixed with 16 grams of oxygen...
what will be the ratio Cp/Cv of the mixture...

how to calculate it?? i thought on the basis of degree of freedom for monoatomic and diatomic mixture...but that can take me to the answer only by approximation...how do we arrive in a a formula that could get me answer...

Aren't they both diatomic?

AM

 

[nomorevishnu]

how?

y do u say that these two are diatomic?

He...its completely satisfied without bonding
He is a noble gas...so y do u say it is diatomic...

moreover someone help me solve the problem yaar...

 

[eutopia]

Monatomic Gases:
Helium, Neon, Argon, Krypton, Xenon, Radon
Single atom, or monatomic, gases have the smallest Specific Heat CV.

Diatomic Gases:
Oxygen, Nitrogen, Hydrogen

 

[Andrew Mason]

y do u say that these two are diatomic?

He...its completely satisfied without bonding
He is a noble gas...so y do u say it is diatomic...

moreover someone help me solve the problem yaar...

Of course you are right. I was seeing He and thinking H.

What is the ratio of the number of He atoms to O2 molecules?

AM

 

[nomorevishnu]

hi

y isn't anyone helping me get the answer?
please if someone can explain the problem to me...it would do a world of good to me...


please please please...the question again...

16 grams of helium gas is mixed with 16 grams of oxygen...
what will be the ratio Cp/Cv of the mixture...

how to calculate it?? i thought on the basis of degree of freedom for monoatomic and diatomic mixture...but that can take me to the answer only by approximation...how do we arrive in a a formula that could get me answer...

 

[Dr.Brain]

nomorevishnu Let helium be the gas 1 and oxygen be the gas 2 .

No. Of moles of Helium: 4 = n1
" " " " oxygen: 0.5 =n2

Lamda factor for a mixture is given by:

L= n1( Cp1) + n2 (Cp2) / n1(Cv1) + n2 (Cv2)

Where Cp1/Cv1=5/3 ( for monoatomic helium)

Cp2/Cv2=7/3 for diatomic oxygen


Answer you get is: 1.62

 

[Andrew Mason]

hi

y isn't anyone helping me get the answer?
please if someone can explain the problem to me...it would do a world of good to me...


please please please...the question again...

16 grams of helium gas is mixed with 16 grams of oxygen...
what will be the ratio Cp/Cv of the mixture...

how to calculate it?? i thought on the basis of degree of freedom for monoatomic and diatomic mixture...but that can take me to the answer only by approximation...how do we arrive in a a formula that could get me answer...

Have you worked out the proportion of numbers of atoms of He to number of molecules of O2?

AM

 

[nomorevishnu]

well...i knew that equation...and the answer


but to find the effective lambda...how do we get to such an equation...any proof...its not given in Resnick and Halliday

 

[Andrew Mason]

well...i knew that equation...and the answer


but to find the effective lambda...how do we get to such an equation...any proof...its not given in Resnick and Halliday

You have to go to basic principles:

$$dU = (Cp - Cv)nT = nRT$$ so:

$$C_p/C_v = \gamma = (C_v + R)/C_v = (1 + R/C_v)$$

So for the mixed gas:

$$(C_{peff} - C_{veff})n_{total}dT = n_{total}RdT$$

$$C_{peff} = (R + C_{veff})$$

(1)$$C_{peff}/C_{veff} = \gamma_{eff} = (R/C_{veff} + 1)$$

Now:

$$Vdp = (C_{vHe}n_{He} + C_{vO_2}n_{O_2})dT = C_{veff}n_{total}dT$$

(2) $$C_{veff} = (C_{vHe}n_{He} + C_{vO_2}n_{O_2})/n_{total}$$

Substitute from (2) into (1).

I get 1.64

AM