Adiabatic Process: Proving Variation of Gamma

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In summary, the adiabatic process refers to a process where there is no heat transfer, and it can be represented by the equation PV^gamma = constant. The value of gamma, which represents the ratio of specific heat at constant pressure to specific heat at constant volume, is 1.4 for diatomic gases and 1.6 for monatomic gases. This value is simply a definition with physical significance. It can be proven theoretically by reading about the simple cases of monatomic and diatomic gases in the Theory of Heat Capacity.
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ajayguhan
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I know that adibatic process means no heat transfer.

i.e., →PV[itex]\gamma[/itex] =constant.

Where [itex]\gamma[/itex] = 1.4 for diatomic gas, [itex]\gamma[/itex]= 1.6 for monoatomic gas.

My question is how [itex]\gamma[/itex]=Cp/Cv ?

And can we prove theoritcally that [itex]\gamma[/itex] = 1.4 for diatomic gas, [itex]\gamma[/itex]= 1.6 for monoatomic gas.
 
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ajayguhan said:
I know that adibatic process means no heat transfer.

i.e., →PV[itex]\gamma[/itex] =constant.

Where [itex]\gamma[/itex] = 1.4 for diatomic gas, [itex]\gamma[/itex]= 1.6 for monoatomic gas.

My question is how [itex]\gamma[/itex]=Cp/Cv ?

Gamma is defined as the ratio of the specific heat at constant pressure to the specific heat at constant temperature.

And can we prove theoritcally that [itex]\gamma[/itex] = 1.4 for diatomic gas, [itex]\gamma[/itex]= 1.6 for monoatomic gas.

http://en.wikipedia.org/wiki/Heat_capacity_ratio
 
  • #3
ajayguhan said:
I know that adibatic process means no heat transfer.

i.e., →PV[itex]\gamma[/itex] =constant.

This equation is only true for an ideal gas undergoing a reversible (i.e., no entropy generation) adiabatic process.

ajayguhan said:
My question is how [itex]\gamma[/itex]=Cp/Cv ?

It is simply a definition for which we found a physical significance (Like work is defined as a force times its displacement).

ajayguhan said:
And can we prove theoritcally that [itex]\gamma[/itex] = 1.4 for diatomic gas, [itex]\gamma[/itex]= 1.6 for monoatomic gas.

Read The simple case of the monatomic gas and Diatomic gas on Theory of heat capacity.
 
  • #4
Thank you for spending time to clarify my doubts. Your answer helped me.
 

FAQ: Adiabatic Process: Proving Variation of Gamma

What is an adiabatic process?

An adiabatic process is a thermodynamic process in which there is no heat transfer between a system and its surroundings. This means that the system is isolated and there is no exchange of heat with the environment.

How is the adiabatic process related to the variation of gamma?

The adiabatic process is related to the variation of gamma through the ideal gas law, which states that the product of pressure and volume of an ideal gas is directly proportional to the temperature and the number of moles of the gas. This relationship is represented by the equation PV = nRT, where gamma (γ) is the ratio of specific heats (Cp/Cv). In an adiabatic process, there is no heat transfer, so the change in temperature is directly related to the change in pressure and volume, which in turn affects the value of gamma.

How is the variation of gamma proven in an adiabatic process?

The variation of gamma is proven in an adiabatic process by measuring the change in temperature, pressure, and volume of a gas under adiabatic conditions. By using the ideal gas law and the relationship between temperature, pressure, and volume in an adiabatic process, the value of gamma can be calculated and compared to the theoretical value for a specific gas. If the calculated value of gamma matches the theoretical value, the variation of gamma has been proven.

What is the significance of proving the variation of gamma in an adiabatic process?

Proving the variation of gamma in an adiabatic process is significant because it provides a better understanding of the behavior of gases under adiabatic conditions. It also helps in the development of thermodynamic models and equations that can be used to predict and analyze the behavior of gases in various industrial and natural processes.

How is the variation of gamma useful in practical applications?

The variation of gamma has many practical applications in various fields such as engineering, meteorology, and geology. It is used to design efficient engines and turbines, predict weather patterns, and understand the behavior of gases in geological processes such as volcanic eruptions. Additionally, the value of gamma is an important parameter in the study of thermodynamics and fluid mechanics, which have a wide range of practical applications in industries such as aerospace, energy, and manufacturing.

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