Adiabatic Expansion Temp: 500K to 6.5x Monatomic, Diatomic (No Vib) & Vibrating

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In an adiabatic expansion of an ideal gas from 500 K to 6.5 times its original volume, the resulting temperature can be calculated using the equation PV^y = constant, where y is determined by the degrees of freedom (f). For a monatomic gas, f equals 3, leading to y = 5/3, while for a diatomic gas without vibrations, f is 5, resulting in y = 7/5. If the diatomic gas includes vibrational modes, f increases to 6, giving y = 8/6. The relationship between pressure, volume, and temperature is established through PV = RT, which integrates into the adiabatic process. This analysis allows for the determination of the final temperature based on the type of gas and its degrees of freedom.
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An ideal gas at 500 K is expanded adiabatically to 6.5 times its original volume. Determine its resulting temperature if the gas is as follows.

(a) monatomic

(b) diatomic (no vibrations)

(c) diatomic (molecules do vibrate)

Anything to get me started?
 
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Start with PV^y = constant where y = 1 + \frac{2}{f}


where f= degrees of freedom

BJ
 
Last edited:
But where does temperature come in the picture?
 
Use PV=RT

Put the value of P from above equation into PV^y , not try it out.

BJ
 

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