Ideal gas - monatomic or diatomic?

[shyguy79]

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!

 

[I like Serena]

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!

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]

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?

 

[I like Serena]

Yep. That is correct.

What would Cp/nR be for a monatomic gas?
And for a diatomic gas?

 

[shyguy79]

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?

 

[I like Serena]

Right. :)

 

[shyguy79]

Thank you so much! I've been stuck on this for ages!

 

[shyguy79]

Just one question though what equation would be referenced for dividing Cp by nR?

 

[I like Serena]

Not sure what you mean...?

You've used 3 of your relevant equations and solved for "f".

 

[shyguy79]

doh! Yeah, just noticed - thanks again!