Thermodynamics, meaning of gamma

In summary, gamma is a ratio of specific heats and it is important when analysing adiabatic processes.
  • #1
AriAstronomer
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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.
 
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  • #2
AriAstronomer said:
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.
[itex]\gamma = C_p/C_v[/itex] is important when analysing adiabatic processes. The ratio appears in the adiabatic condition:

[tex]PV^\gamma = Constant[/tex]

So, for an adiabatic compression:

[tex]P_f/P_i = (V_i/V_f)^\gamma[/tex]

[tex]\ln{(P_f/P_i)} = \ln{(V_i/V_f)^\gamma} = \gamma\ln{(V_i/V_f)}[/tex]

AM
 
  • #3
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...?
 
  • #4
AriAstronomer said:
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
 
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Hi there,

In thermodynamics, gamma (γ) is known as the ratio of specific heats, or the ratio of the heat capacity at constant pressure (cp) to the heat capacity at constant volume (cv). This ratio is important because it relates the change in temperature to the change in internal energy of a substance.

When we divide cp by cv, we are essentially comparing the amount of heat required to raise the temperature of a substance at constant pressure to the amount of heat required to raise the temperature of the same substance at constant volume. This ratio allows us to better understand how a substance will behave under different conditions, such as changing pressure or volume.

In essence, the ratio of specific heats (gamma) is a measure of the efficiency with which heat is transferred into or out of a substance. A higher value of gamma means that the substance is better at absorbing or releasing heat, while a lower value indicates that the substance is less efficient at heat transfer.

I hope this helps to clarify the meaning of gamma in thermodynamics. Let me know if you have any further questions. Good luck with your studies!
 

1. What is thermodynamics?

Thermodynamics is the branch of science that deals with the relationships between heat, energy, and work. It also studies how these factors affect physical properties and behavior of matter.

2. What is the meaning of gamma in thermodynamics?

In thermodynamics, gamma (γ) refers to the ratio of the specific heat capacities at constant pressure and constant volume of a gas. It is also known as the adiabatic index or ratio of specific heats.

3. How is gamma calculated in thermodynamics?

Gamma is calculated by dividing the specific heat at constant pressure (Cp) by the specific heat at constant volume (Cv). So, γ = Cp/Cv.

4. What is the significance of gamma in thermodynamics?

The value of gamma is important in understanding the behavior of gases. It is used in various thermodynamic equations, such as the ideal gas law and the adiabatic processes equation. It also helps in determining the speed of sound in a gas.

5. How does gamma affect the properties of a gas?

The value of gamma affects the compressibility, thermal expansion, and speed of sound of a gas. It also plays a role in determining the efficiency of certain thermodynamic processes, such as the efficiency of an Otto cycle in an internal combustion engine.

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