# Basis of degree of freedom for monoatomic and diatomic mixture

• nomorevishnu
In summary, you can calculate the lambda factor for a mixture of monoatomic and diatomic gases by using the equation: lambda = (Cp - Cv)nT.
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...

nomorevishnu said:
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

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...

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

Diatomic Gases:
Oxygen, Nitrogen, Hydrogen

nomorevishnu said:
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

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...

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...

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

nomorevishnu said:
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...

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

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

nomorevishnu said:
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

## 1. What is the basis of degree of freedom for monoatomic and diatomic mixture?

The basis of degree of freedom for monoatomic and diatomic mixture is the number of independent variables that can be varied to describe the state of the mixture. This is determined by the number of particles and the type of interactions between them.

## 2. How are the degrees of freedom different for monoatomic and diatomic mixtures?

Monoatomic mixtures have three degrees of freedom, corresponding to the three dimensions of space. Diatomic mixtures have five degrees of freedom, as they also have rotational and vibrational motion in addition to translational motion.

## 3. What is the relationship between degrees of freedom and the number of particles in a mixture?

The number of particles in a monoatomic or diatomic mixture does not affect the number of degrees of freedom. The degrees of freedom are determined by the type of particles and their interactions, not the quantity.

## 4. Can the degrees of freedom change for a monoatomic or diatomic mixture?

No, the degrees of freedom for a monoatomic or diatomic mixture are fixed and do not change unless there is a change in the type of particles or their interactions.

## 5. How does the concept of degrees of freedom apply to the study of thermodynamics?

The concept of degrees of freedom is important in thermodynamics as it helps to determine the number of variables needed to fully describe the state of a system. This allows for the prediction and analysis of thermodynamic processes and properties of mixtures.

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