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

In summary, for an ideal gas undergoing an isobaric process, the change in internal energy can be calculated using ΔU=Q-PΔV, and the molar specific heat capacity CP can be determined using the equation Cp/Cv=(Q-PΔV)/Q, where Cp-Cv=R for an ideal gas.
  • #1
BOAS
552
19

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, Cp 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!
 
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  • #2
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 cv, from which you can extract cp.
 
  • #3
BOAS said:

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, Cp 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=CpΔT and ΔU=CvΔT. So,
ΔH/ΔU=Cp/Cv=(Q-PΔV)/Q. You also know that Cp-Cv for an ideal gas is equal to R. This should give you enough information to determine Cp.
 

1. What is specific heat capacity?

Specific heat capacity is a measure of the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius. It is usually denoted by the symbol "C" and has units of Joules per gram per degree Celsius (J/g°C).

2. How is specific heat capacity different for a non-monatomic ideal gas?

For a non-monatomic ideal gas, the specific heat capacity is dependent on the number of atoms in the gas molecule. This is because the atoms can vibrate in multiple directions, allowing for more ways to store thermal energy compared to a monatomic gas.

3. What is the equation for finding specific heat capacity of a non-monatomic ideal gas?

The equation for finding specific heat capacity of a non-monatomic ideal gas is: C = (f/2)R, where "C" is the specific heat capacity, "f" is the degree of freedom of the gas molecule, and "R" is the gas constant.

4. How do you determine the degree of freedom of a gas molecule?

The degree of freedom of a gas molecule can be determined by the number of independent ways it can move or vibrate. For a non-monatomic gas, the degree of freedom is equal to 3N, where N is the number of atoms in the molecule.

5. Can the specific heat capacity of a non-monatomic ideal gas change?

Yes, the specific heat capacity of a non-monatomic ideal gas can change with temperature. This is because as the temperature increases, the gas molecules gain more kinetic energy and have a higher degree of freedom, leading to an increase in specific heat capacity.

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