Universal gas, Boltzmann's constant

Evilinside

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?

FredGarvin

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.

Evilinside

oh, I don't think came across any formula concerning enthalpy yet but it makes sense in equation form.

FredGarvin

Enthalpy is a very useful term. If you get into thermodynamics you will become very familiar with it.