Universal gas, Boltzmann's constant

In summary, The Universal Gas Constant defines the relationship between moles, Kelvin, and Joules. However, an increase in Kelvin does not necessarily mean an increase in Joules, which goes against the kinetic theory. Boltzmann's Constant states that each atom has 1.38x amount of Joules per Kelvin. When defining enthalpy using the ideal gas equation of state, we can see that C_p - C_v = R, meaning that for all ideal gases, the difference between C_p and C_v is a constant. Enthalpy is an important concept in thermodynamics.
  • #1
Evilinside
20
0
I understand the formulas involved and numerical values of these constants and in the respective units . However I'm still having troubling understanding exactly what it is these two constants define. Does Universal gas constant say that For every mol times Kelvin there is 8.315J ? I don't think that makes sense since an increase in kelvin should actually decrease the amount joules, since K is in the denominator, which I believe then defies a portion of kinetic theory. Then Boltzmann's constant is it saying that every atom will have 1.38x amount of joules per kelvin?
 
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  • #2
R is defined by this relationship going back to the definition of enthalpy:

[tex]h = u + \frac{p}{\rho}[/tex] and the form of ideal gas equation of state [tex]p =\rho RT[/tex] You get:

[tex]h = u + RT[/tex]

If you differentiate with respect to temperature:

[tex]dh = du + R dT[/tex]

[tex]\frac{dh}{dT} = \frac{du}{dT} + R[/tex]

From relations for ideal gases...

[tex]C_v = \frac{du}{dT}[/tex] and [tex]C_p = \frac{dh}{dT}[/tex]

we can say that [tex]C_p = C_v + R[/tex] or

[tex]C_p - C_v = R[/tex]

This is important because that says that for all ideal gasses, the difference between [tex]C_p[/tex] and [tex]C_v[/tex] is a constant.
 
  • #3
oh, I don't think came across any formula concerning enthalpy yet but it makes sense in equation form.
 
  • #4
Enthalpy is a very useful term. If you get into thermodynamics you will become very familiar with it.
 

1. What is universal gas constant?

The universal gas constant, denoted by R, is a physical constant that relates the energy of a gas to its temperature and pressure. It is also known as the molar gas constant and has the value of 8.314 J/mol*K.

2. What is Boltzmann's constant?

Boltzmann's constant, denoted by k, is a physical constant that relates the average kinetic energy of particles in a gas to its temperature. It has the value of 1.380649 x 10^-23 J/K.

3. How are universal gas constant and Boltzmann's constant related?

They are related through the equation R = N*k, where N is Avogadro's number. This equation shows that the universal gas constant is the product of Avogadro's number and Boltzmann's constant.

4. What is the significance of these constants?

These constants are important in the study of thermodynamics and statistical mechanics. They allow us to relate the macroscopic properties of gases, such as temperature and pressure, to the microscopic behavior of their particles.

5. Are these constants truly universal?

Yes, both the universal gas constant and Boltzmann's constant are considered to be universal constants, meaning that they have the same value in all systems and are not dependent on the specific gas or particles being studied.

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