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

[Banyans]

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.

 

[mfb]

What is Cp for an ideal monoatomic gas?

 

[BvU]

Hello Banyans,

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 ?

 

[Banyans]

What is Cp for an ideal monoatomic gas?

5/2R?

 

[Banyans]

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?

 

[mfb]

5/2R?

That is Cp for a monoatomic gas, right. Does that match the result you got for the unknown gas?

Cp=Cv+nR

That formula is not right. Use specific heat capacities or use total heat capacities, but do so in a consistent way.