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March 29, 2015

March 29, 2015

Posted by **david** on Wednesday, January 26, 2011 at 1:50am.

- physics -
**drwls**, Wednesday, January 26, 2011 at 5:36amIn an isothermal process, P*V = contant

In an adiabatic process (at constant entropy), P*V^gamma = constant

where gamma is the specific heat ratio, Cp/Cv. (Adiabatic expansions are isentropic unless they are into a vacuum and do no work)

For neon and other monatomic gases,

gamma = 5/3.

Original To = 273 K

Original Po = 1.00 atm

Original Vo = 3*22.4 = 67.2 liters

After the isothermal compression,

V1 = 12.77 liter = 0.19 Vo

T1 = 273 K

P1 = (1/0.19)Po = 5.26 Po

After the adiabatic expansion,

V2 = Vo

P2*V2^5/3 = P1*V1^5/3

P2/P1 = (V1/V2)^5/3 = (V1/V0)^5/3

= 0.19^5/3 = 0.0628

P2 = 0.0628 *5.26 = 0.330 atm

P2*V2/T2 = Po*Vo/To

T2 = (P2/Po)(V2/Vo)*To

= 0.330* 273 = 90.2 K

Highest P = Po = 5.26 atm

Lowest P = P2 = 0.330 atm

Highest T = To

Lowest T = T2

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