Ideal gas - monatomic or diatomic?

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Homework Help Overview

The discussion revolves around determining whether a gas is monatomic or diatomic based on its heat capacity values during a heating process at constant pressure. The scenario involves 5 moles of an ideal gas being heated from 300K to 500K, with a specified amount of heat transferred.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between heat capacity at constant pressure and the type of gas by calculating Cp and comparing it to theoretical values for monatomic and diatomic gases. Questions arise about the calculations and the significance of dividing Cp by nR.

Discussion Status

Participants have engaged in calculations and have reached a point where they suggest that the gas is diatomic based on the derived values. There is ongoing clarification regarding the equations used and their implications, but no explicit consensus has been stated.

Contextual Notes

There is a focus on the definitions and values of molar heat capacities for different types of gases, as well as the assumptions inherent in the ideal gas model. Participants express some uncertainty about the calculations and the reasoning behind them.

shyguy79
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Homework Statement



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

Homework 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

The Attempt at a Solution


No idea where to start... help please!
 
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shyguy79 said:

Homework Statement



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

Homework 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

The Attempt at a Solution


No idea where to start... help please!

Hi shyguy79! :smile:

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?
 
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?
 
Yep. That is correct.

What would Cp/nR be for a monatomic gas?
And for a diatomic gas?
 
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?
 
Right. :)
 
Thank you so much! I've been stuck on this for ages!
 
Just one question though what equation would be referenced for dividing Cp by nR?
 
Not sure what you mean...?

You've used 3 of your relevant equations and solved for "f".
 
  • #10
doh! Yeah, just noticed - thanks again!
 

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