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hydey
Joined: 29 Jan 2012 Posts: 2 Location: United Kingdom

Posted: Mon Jan 30, 2012 1:10 am Post subject: Gas is monatomic or diatomic? 


Good morning,
I am really stuck on a physics question for my mock exam that i am currently taking. I have been doing this paper since 5pm today, it's not 1 am and I cannot for the life of me find any pointers online so I'm wondering if you can please shed some light on this question for me.
AS FOLLOWS: "a sample consisting of 5 moles of an ideal gas at temperature of 300 K and a pressure of 1.00 X 10^5 Pa is heated to a temperature of 500 K at constant pressure. The amount of heat transferred to the gas is 29.1 kJ."
The question is:
Q. Determine whether the gas is monatomic or diatomic through consideration of the values of the molar heat capacity at constant pressure, C p,m and at constant volume, C v,m.
If you can please shed some light or guide me in the right direction, let alone provide the answer i will be very happy.
Thank you for reading. 

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hepcj Site Admin
Joined: 23 Jun 2007 Posts: 125

Posted: Tue Jan 31, 2012 1:10 am Post subject: 


Overview: You need to be able to calculate the ratio of the heat capacities at constant pressure and constant volume. The value of the ratio will determine whether the gas is monatomic or diatomic.
The information you have been given is as follows:
n = 5;
Ti = 300K
Pi = 1x10e5 Pa
Tf = 500K
Q = 29.1 kJ
Using the first law of thermodynamics:
dU + dW = Q
deltaU + P(VfVi) = n Cv (Tf  Ti) where f and i mean final and initial respectively. For constant volume (Vf  Vi) = 0;
Therefore, deltaU = n Cv (Tf  Ti)
For constant pressure
deltaU + P(Vf  Vi) = n Cp (Tf Ti)
nCv (Tf  Ti) + P(Vf Vi) = n Cp (TfTi)
and P(Vf  Vi) = n R (Tf  Ti)
n Cv (Tf Ti) +n R(Tf  Ti) = n Cp (Tf  Ti)
Cv + R = Cp
So the heat capacities differ by an addition of R, the molar gas constant.
Using the information you can calculate the values of Cp and Cv and thus the ratio Cp/Cv is around 1.66 for a monatomic gas and lower for a diatomic gas. 

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