Determining Cv Value for Ideal Gases

[Jaydude]

Stuck on part of this question regarding Cv value:

I don't understand how one can get the value for Cv,

I tried saying Cp - Cv = R (1)
Cp/Cv = 1.5.so rearrange gives Cp=1.5Cv (2)

Now sub 2 into 1 and that gives 0.5Cv = R
But according to solutions that's wrong, Cv is 1010 and I can't get that value!

Please point me in the right direction,

Kind regards ,

Jay

 

[Chestermiller]

For air (which is diatomic), Cv = 2.5 R.

Chet

 

[Jaydude]

For air (which is diatomic), Cv = 2.5 R.

Chet

I see, if R has value 287, then Cv is 717.5 - still not the value used according the solutions which is 1010

Jay

 

[Chestermiller]

I see, if R has value 287, then Cv is 717.5 - still not the value used according the solutions which is 1010

Jay

The 1010 value is the constant pressure heat capacity, not the constant volume heat capacity. Divide it by 1.4 to get the constant volume heat capacity.

Chet

 

[Jaydude]

The 1010 value is the constant pressure heat capacity, not the constant volume heat capacity. Divide it by 1.4 to get the constant volume heat capacity.

Chet

My mistake and confusion - sorry!

I want to start again to make it clear for myself:

In the solutions he uses Cp - R rather than Cv, why? We could have just used value for Cv like you said equal to 2.5R

Ignoring above and continuing like the solutions, how is Cp value obtained? Eg you said it for Cv, what about Cp ? I guess we could times Cv by 1.5 but that defeats the purpose of using Cp - R when we already knew the value of Cv!

(When I try your way of using Cv, the final answer varies slightly)

Kind regards,

 

[Chestermiller]

My mistake and confusion - sorry!

I want to start again to make it clear for myself:

In the solutions he uses Cp - R rather than Cv, why? We could have just used value for Cv like you said equal to 2.5R

I don't know why. To figure that out, I would have to be able to read his mind.

Ignoring above and continuing like the solutions, how is Cp value obtained? Eg you said it for Cv, what about Cp ? I guess we could times Cv by 1.4 but that defeats the purpose of using Cp - R when we already knew the value of Cv!

For an ideal gas, Cp = Cv + R. Cv is determined by the number of degrees of freedom of the molecule: Cv=0.5fR. For air at typical temperatures, f = 5, including 3 translational degrees of freedom and 2 rotational degrees of freedom. Even if these relationships are not used, one can always measure the heat capacity of a material.

Chet

 

[Jaydude]

I don't know why. To figure that out, I would have to be able to read his mind.

For an ideal gas, Cp = Cv + R. Cv is determined by the number of degrees of freedom of the molecule: Cv=0.5fR. For air at typical temperatures, f = 5, including 3 translational degrees of freedom and 2 rotational degrees of freedom. Even if these relationships are not used, one can always measure the heat capacity of a material.

Chet

After researching that I can see what you did there.
For diatomic molecules which is air use Cv = 2.5R . To determine Cp simply use Cp/Cv = k, and usually k is taken as 1.4 unless given.

I used this technique on other questions and it works every time so far, including the question posted above - brilliant!

Thank you!