Is the Molar Specific Heat of Air Similar to Hydrogen?

  • #1
Karfen
1
0
Homework Statement
Estimate the molar specific heat of the air at constant volume Cv by taking into account
major molecules in the air. Plot it as a function of absolute temperature and discuss its
significance.
Relevant Equations
The major chemical elements of air are nitrogen(78%) and oxygen(22%).

The molar specific heat of the air at constant volume for diatomic molecule:
Cv=3/2R (Low Temperature)
Cv=5/2R(High Temperature)
Cv=7/2R(Higher Temperature)
And this is the Cv graph for hydrogen:

1700206012610.png

I think the Cv graph for air is similar with this graph. But I don't know the answer, can someone tell me?
 
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  • #2
Oxygen and nitrogen are somewhat similar to hydrogen for the purpose of this question.

What is room temperature in Kelvin, very roughly? Where in this graph are we?
 
  • #3
mfb said:
Oxygen and nitrogen are somewhat similar to hydrogen for the purpose of this question.
Is that true? At https://en.wikipedia.org/wiki/Molar_heat_capacity I read:
"For the rotational degrees of freedom, the thawing temperature is usually a few tens of kelvins (although with a very light molecule such as hydrogen the rotational energy levels will be spaced so widely that rotational heat capacity may not completely "unfreeze" until considerably higher temperatures are reached)."
 

FAQ: Is the Molar Specific Heat of Air Similar to Hydrogen?

What is the molar specific heat at constant volume (Cv) for air?

The molar specific heat at constant volume (Cv) for air, which is primarily composed of diatomic gases like nitrogen (N2) and oxygen (O2), is approximately 20.8 J/(mol·K).

How do you calculate the molar specific heat at constant volume (Cv) for air?

To calculate the molar specific heat at constant volume (Cv) for air, you can use the formula Cv = (f/2)R, where f is the degrees of freedom for the gas molecules and R is the universal gas constant (8.314 J/(mol·K)). For diatomic gases like those in air, f is typically 5, leading to Cv = (5/2)R ≈ 20.8 J/(mol·K).

Why is it important to know the molar specific heat at constant volume (Cv) for air?

Knowing the molar specific heat at constant volume (Cv) for air is important for various applications in thermodynamics, including understanding energy transfer, calculating changes in internal energy, and designing systems involving gas processes, such as engines and HVAC systems.

How does the molar specific heat at constant volume (Cv) differ from the molar specific heat at constant pressure (Cp) for air?

The molar specific heat at constant volume (Cv) differs from the molar specific heat at constant pressure (Cp) because Cp includes additional energy required to do work against the external pressure. For air, Cp is approximately 29.1 J/(mol·K), which is higher than Cv due to this extra energy requirement. The relationship between them is given by Cp = Cv + R.

Can the molar specific heat at constant volume (Cv) for air change with temperature?

Yes, the molar specific heat at constant volume (Cv) for air can change with temperature, especially at higher temperatures where the vibrational modes of the diatomic molecules become excited. At standard conditions, however, Cv is typically considered constant for simplicity in calculations.

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