Thermodynamics, meaning of gamma

[AriAstronomer]

Hey guys, I just had a conceptual question as to the meaning of gamma in thermodynamics. I mean, I know that gamma = cp/cv, where cp = at constant pressure the amount of heat to raise one kg of substance 1 degree, and cv = amount of heat to raise one kg of substance 1 degree at constant volume, but when dividing cp/cv, what does that mean? I feel like the "amount of heat to raise one kg of substance 1 degree" gets canceled so to speak, and we are left with...constant pressure/constant volume?


Any help would be appreciated.

 

[Andrew Mason]

Hey guys, I just had a conceptual question as to the meaning of gamma in thermodynamics. I mean, I know that gamma = cp/cv, where cp = at constant pressure the amount of heat to raise one kg of substance 1 degree, and cv = amount of heat to raise one kg of substance 1 degree at constant volume, but when dividing cp/cv, what does that mean? I feel like the "amount of heat to raise one kg of substance 1 degree" gets canceled so to speak, and we are left with...constant pressure/constant volume?

Any help would be appreciated.

$\gamma = C_p/C_v$ is important when analysing adiabatic processes. The ratio appears in the adiabatic condition:

$$PV^\gamma = Constant$$

So, for an adiabatic compression:

$$P_f/P_i = (V_i/V_f)^\gamma$$

$$\ln{(P_f/P_i)} = \ln{(V_i/V_f)^\gamma} = \gamma\ln{(V_i/V_f)}$$

AM

 

[AriAstronomer]

Yes, mathematically I am quite familiar with what the equations are and where it is relevant. What I am curious is to the meaning of gamma. What is the significant of cp/cv? I know it has no units, perhaps it is simply some arbitrary constant that happens to make some equation true without any meaning? But there has to be some meaning to it, or why does it exist...?

 

[Andrew Mason]

Yes, mathematically I am quite familiar with what the equations are and where it is relevant. What I am curious is to the meaning of gamma. What is the significant of cp/cv? I know it has no units, perhaps it is simply some arbitrary constant that happens to make some equation true without any meaning? But there has to be some meaning to it, or why does it exist...?

It is not arbitrary and it is not constant (it depends upon the gas and it can vary with temperature). It is just a ratio of specific heats. It is greater than 1 because the specific heat at constant pressure is greater than the specific heat at constant volume by the amount R. Cp-Cv=R. It "exists" because it is useful. In other words it is useful so we use it.

Its "meaning" depends on the context in which it is used. For a given heat flow at constant pressure, it represents the ratio of heat flow to change in internal energy. For an adiabatic process it is the factor in the adiabatic condition. It doesn't represent a physical quantity so it does not "exist" physically. It is just a ratio. What does the charge to mass ratio of a proton mean?

AM