Adiabatic Process: Proving Variation of Gamma

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Discussion Overview

The discussion revolves around the concept of adiabatic processes in thermodynamics, specifically focusing on the definition and theoretical proof of the heat capacity ratio, gamma (γ), for different types of gases. Participants explore the relationship between gamma, specific heats, and the conditions under which the adiabatic process equations apply.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that an adiabatic process involves no heat transfer and is characterized by the equation PVγ = constant.
  • Participants inquire about the definition of gamma as the ratio of specific heats (Cp/Cv) and seek a theoretical proof for its values: γ = 1.4 for diatomic gases and γ = 1.6 for monoatomic gases.
  • One participant notes that the equation PVγ = constant is valid for ideal gases undergoing a reversible adiabatic process, highlighting the importance of entropy considerations.
  • There is a suggestion that gamma is a defined ratio that has physical significance, similar to other definitions in physics.
  • Links to external resources, such as Wikipedia, are provided for further reading on heat capacity ratios.

Areas of Agreement / Disagreement

Participants express similar questions regarding the definition and proof of gamma, but there is no consensus on how to theoretically establish the specific values for different gases. The discussion remains unresolved regarding the theoretical proof of gamma's values.

Contextual Notes

The discussion does not clarify the assumptions underlying the definitions of specific heats or the conditions for the adiabatic process. There are references to external resources that may provide additional context but do not resolve the theoretical inquiries posed.

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
 
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.
 
Thank you for spending time to clarify my doubts. Your answer helped me.
 

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