Finding specific heat capacity of a non-monatomic (ideal gas)

[BOAS]

Homework Statement

Suppose that 31.4 J of heat is added to an ideal gas. The gas expands at a constant
pressure of 1.40x10⁴ Pa while changing its volume from 3.00x10⁴ to 8.00x10⁴ m³.
The gas is not monatomic, so the relation CP = 5/2R does not apply. (a) Determine the
change in the internal energy of the gas. (b) Calculate its molar specic heat capacity
CP .

Homework Equations

The Attempt at a Solution

I have completed part a) using the knowledge that it is an isobaric process, but I'm a bit unsure of my answer for b)

My textbook says that for a diatomic ideal gas, C_p is given by 7/2 R, but the question only says the gas is not monatomic.

Is there a piece of info I'm missing?

Thanks!

 

[CAF123]

Because U is a state variable, you can define a path between the initial and final states of the gas where V is a constant. This will allow you to find c_v, from which you can extract c_p.

 

[Chestermiller]

Homework Statement

Suppose that 31.4 J of heat is added to an ideal gas. The gas expands at a constant
pressure of 1.40x10⁴ Pa while changing its volume from 3.00x10⁴ to 8.00x10⁴ m³.
The gas is not monatomic, so the relation CP = 5/2R does not apply. (a) Determine the
change in the internal energy of the gas. (b) Calculate its molar specic heat capacity
CP .

Homework Equations

The Attempt at a Solution

I have completed part a) using the knowledge that it is an isobaric process, but I'm a bit unsure of my answer for b)

My textbook says that for a diatomic ideal gas, C_p is given by 7/2 R, but the question only says the gas is not monatomic.

Is there a piece of info I'm missing?

Thanks!

Just apply the constant pressure version of the first law: ΔU=Q-PΔV. Also, since ΔH=ΔU+Δ(PV), which for this constant pressure process becomes ΔH=ΔU+PΔV. So, for this process ΔH=Q. For an ideal gas, ΔH=C_pΔT and ΔU=C_vΔT. So,
ΔH/ΔU=C_p/C_v=(Q-PΔV)/Q. You also know that C_p-C_v for an ideal gas is equal to R. This should give you enough information to determine C_p.