Adiabatic Process: Proving Variation of Gamma

[ajayguhan]

I know that adibatic process means no heat transfer.

i.e., →PV^\gamma =constant.

Where \gamma = 1.4 for diatomic gas, \gamma= 1.6 for monoatomic gas.

My question is how \gamma=C_p/C_v ?

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

 

[SteamKing]

I know that adibatic process means no heat transfer.

i.e., →PV^\gamma =constant.

Where \gamma = 1.4 for diatomic gas, \gamma= 1.6 for monoatomic gas.

My question is how \gamma=C_p/C_v ?

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 \gamma = 1.4 for diatomic gas, \gamma= 1.6 for monoatomic gas.

http://en.wikipedia.org/wiki/Heat_capacity_ratio

 

[jack action]

I know that adibatic process means no heat transfer.

i.e., →PV^\gamma =constant.

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

My question is how \gamma=C_p/C_v ?

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

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

Read The simple case of the monatomic gas and Diatomic gas on Theory of heat capacity.

 

[ajayguhan]

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