What is the molar heat capacity of an ideal gas at constant pressure and volume?

AI Thread Summary
The discussion revolves around calculating the molar heat capacities of an ideal gas at constant pressure (C_p,m) and constant volume (C_v,m) after supplying 117 J of heat to 2.00 moles of gas, resulting in a temperature increase of 2.00 K. The calculated C_p,m is 29.25 J/K mole, leading to the conclusion that C_v,m is 2.52 R. Participants discuss the characteristics of monatomic versus diatomic gases, noting that for a monatomic gas, C_p should equal 5/2 R. The conversation emphasizes the importance of using consistent formulas for specific and total heat capacities to determine the gas type accurately, ultimately suggesting that the gas is likely monatomic based on the derived values.
Banyans
Messages
3
Reaction score
0

Homework Statement



117 J of energy is supplied as heat to 2.00 moles of an ideal gas at constant
pressure, the temperature rises by 2.00 K. Calculate the molar heat capacity at
constant pressure C_p,m and the molar heat capacity at constant volume C_v,m
for the gas. Is the gas monatomic or diatomic?

Homework Equations


PV = nRT
ΔQ = n Cp ΔT

The Attempt at a Solution


ΔQ = 117 J
n = 2 moles
ΔT = 2 K

ΔQ = n Cp ΔT = n αR ΔT
Cp = ΔQ/ (nΔT) = 29.25 J/K mole
Cp/R = 3.52

For ideal gases equation of state is
PV = nRT,
and work performed by the gas in isobaric process is
dA = PdV = nRdT,
which means Cv = Cp - R = 2.52 R.

But I have no idea how to relate this information to work out if its diatomic or monatomic.
 
Physics news on Phys.org
What is Cp for an ideal monoatomic gas?
 
Hello Banyans, :welcome:

Hard to give a hint here without spoiling the exercise. Don't the values of ##{7\over 2}## and ##{5\over 2}## ring a bell ? What would they be for an ideal monatomic gas ?
 
mfb said:
What is Cp for an ideal monoatomic gas?
5/2R?
 
So would I proceed in the following way?

Cp=29.25

Cp=Cv+nR
29.25=Cv+2(8.31451)

so

Cv=12.621

So there fore its a monoatomic gas? since Cv=3/2R?
 
Banyans said:
5/2R?
That is Cp for a monoatomic gas, right. Does that match the result you got for the unknown gas?
Banyans said:
Cp=Cv+nR
That formula is not right. Use specific heat capacities or use total heat capacities, but do so in a consistent way.
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'Collision of a bullet on a rod-string system: query'
In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top