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Unformatted text preview: ME320 Thermodynamics Homework set #11 Due: Wednesday 12/10/03 at 5:00 PM 1. For a gas with specific free energy f given by f = f ( T, υ ) = a υ RT ln( υ b ) + φ ( T ) , with a and b constant, R the gas constant, and φ an arbitrary function, obtain expressions for the specific entropy s and the pressure P . For what choices of a and b does the given f describe an ideal gas? Solution: Since s = ∂f ( T, ν ) ∂T and P = ∂f ( T, ν ) ∂ν , it follows that s = R ln( ν b ) d Φ( T ) dT and P = a ν 2 + RT ν b . Since, for an ideal gas, Pν = RT , f describes an ideal gas only for a = b = 0. 2. Show that the Gibbs free energy g = g ( T, p ) for an ideal gas with constant specific heats can be exprressed in the form g ( T, P ) = C P T parenleftbigg 1 ln T T parenrightbigg + RT ln P P , with C P the specific heat at constant pressure, R the gas constant, T a reference temerpature, and P a reference pressure. Solution: In general, the specific entropy s and specific volume ν are determined from g via s = ∂g ( T, P ) ∂T and ν = ∂g ( T, P ) ∂P ....
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 Spring '08
 Shen
 Thermodynamics, Entropy, Heat, Qin

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