# 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?

## Answers and Replies

R is defined by this relationship going back to the definition of enthalpy:

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

$$h = u + RT$$

If you differentiate with respect to temperature:

$$dh = du + R dT$$

$$\frac{dh}{dT} = \frac{du}{dT} + R$$

From relations for ideal gases...

$$C_v = \frac{du}{dT}$$ and $$C_p = \frac{dh}{dT}$$

we can say that $$C_p = C_v + R$$ or

$$C_p - C_v = R$$

This is important because that says that for all ideal gasses, the difference between $$C_p$$ and $$C_v$$ is a constant.

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