Solving Adiabatic Process for Diatomic Gas: Volume & Temp Change

[HemaZ]

1. The problem statement,
During the compression stroke of a certain gasoline engine, the pressure increases from 1 atm to 20 atm. If the process is adiabatic and the air–fuel mixture behaves as a diatomic ideal gas,
(a) by what factor does the volume change and
(b) by what factor does the temperature change?




when i searched on the internet for Cv and Cp for diatmoic gas i found it to be 5/2 R



and i don't know why they consider the transitional and rotational motion only for the degree of freedoms and why they neglect the vibration motion i think it should be 7/2 R for Cv and 9/2 R for Cp

 

[ehild]

The Equipartition Principle applies only at temperatures where the thermal energy K_BT is well above the excitation energy of the vibrational mode of the molecule. The energy of vibration motion of two-atomic molecules is in the range 0.2-0.5 eV.

See

ehild

 

[TheAustrian]

1. The problem statement,
During the compression stroke of a certain gasoline engine, the pressure increases from 1 atm to 20 atm. If the process is adiabatic and the air–fuel mixture behaves as a diatomic ideal gas,
(a) by what factor does the volume change and
(b) by what factor does the temperature change?




when i searched on the internet for Cv and Cp for diatmoic gas i found it to be 5/2 R



and i don't know why they consider the transitional and rotational motion only for the degree of freedoms and why they neglect the vibration motion i think it should be 7/2 R for Cv and 9/2 R for Cp

Basically, what they are saying is "Ignore Quantum effects" And then you have 5 degrees of freedom. So then you have to use 5/2 instead of 7/2. Basically, it's just to save you time.

 

[HemaZ]

ok thanks ehild And TheAustrian i got it :)

 

[Andrew Mason]

Basically, what they are saying is "Ignore Quantum effects" And then you have 5 degrees of freedom. So then you have to use 5/2 instead of 7/2. Basically, it's just to save you time.

?? There would be 7 degrees of freedom if one was to "ignore quantum effects". The Cv of an ideal diatomic gas is 5/2 except at very low and very high temperatures BECAUSE of quantum effects (e.g. the "freezing out" of vibrational modes except at very high temperatures), as shown in ehild's excellent chart.

AM