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

Suppose 3 mols of neon (an ideal monatomic gas) at STP are compressed slowly and isothermally to 0.19 the original volume. The gas is then allowed to expand quickly and adiabatically back to its original volume. Find the highest temperature attained by the gas. Find the lowest temperature attained by the gas. Find the highest pressure attained by the gas. Find the lowest pressure attained by the gas.

- physics -
**drwls**, Wednesday, January 26, 2011 at 5:36am
In 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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