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Ideal gas - monatomic or diatomic?

by shyguy79
Tags: diatomic, ideal, monatomic
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shyguy79
#1
Jan15-12, 02:16 PM
P: 102
1. The problem statement, all variables and given/known data

5 moles of an idea gas at 300K at a pressure of 1.00 x 10^5 Pa is heated to 500K at constant pressure. The amount of heat transferred is 29.1kJ.

Determine whether a gas is monatomic or diatomic through consideration of the values of the molar heat capacity at constant pressure C sub c,m and at C sub v,m

2. Relevant equations
PV = nRT
C = dQ/dT
Cp = Cv + nR
Cv = f/2 nR where f = 3 for monatomic gas and f = 5 for diatomic gas

3. The attempt at a solution
No idea where to start... help please!
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#2
Jan15-12, 03:09 PM
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Quote Quote by shyguy79 View Post
1. The problem statement, all variables and given/known data

5 moles of an idea gas at 300K at a pressure of 1.00 x 10^5 Pa is heated to 500K at constant pressure. The amount of heat transferred is 29.1kJ.

Determine whether a gas is monatomic or diatomic through consideration of the values of the molar heat capacity at constant pressure C sub c,m and at C sub v,m

2. Relevant equations
PV = nRT
C = dQ/dT
Cp = Cv + nR
Cv = f/2 nR where f = 3 for monatomic gas and f = 5 for diatomic gas

3. The attempt at a solution
No idea where to start... help please!
Hi shyguy79!

In a constant pressure process you have Cp=dQ/dT.
Can you calculate Cp from that?
What would you get if you divide Cp by nR?
shyguy79
#3
Jan15-12, 03:16 PM
P: 102
Where dQ = 29.1x10^3 and dT = 200K then Cp = 145.5 J K^-1

Is nR = 5 x 8.314 = 41.57 ???? but why would you do this?

so Cp/nr = 3.5 ???? How does this relate?

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#4
Jan15-12, 03:19 PM
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Ideal gas - monatomic or diatomic?

Yep. That is correct.

What would Cp/nR be for a monatomic gas?
And for a diatomic gas?
shyguy79
#5
Jan15-12, 03:37 PM
P: 102
Cp = (f/2 +1) nR so then Cp/nR = (f/2 +1)

so for a monatomic gas... 3/2 + 1 = 2.5
for a diatomic gas... 5/2 +1 = 3.5

so the gas is diatomic?
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#6
Jan15-12, 03:39 PM
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Right. :)
shyguy79
#7
Jan15-12, 03:40 PM
P: 102
Thank you so much! I've been stuck on this for ages!
shyguy79
#8
Jan15-12, 04:04 PM
P: 102
Just one question though what equation would be referenced for dividing Cp by nR?
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#9
Jan15-12, 04:11 PM
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Not sure what you mean...?

You've used 3 of your relevant equations and solved for "f".
shyguy79
#10
Jan15-12, 04:12 PM
P: 102
doh! Yeah, just noticed - thanks again!


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