The speed of propagation of a small pressure pulse or sound wave in a fluid, v S

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The speed of propagation of a small pressure pulse or sound wave in a fluid, vS, can be shown to be equal to

US   S

where ρ is the molar density. 

a. Show that an alternative expression for the sonic velocity is

Us = V *(), (), V2 V P

where γ = CP/CV.

b. Show that γ = 1+R/CV for both the ideal gas and a gas that obeys the Clausius equation of state

P(V - b) = RT

and that γ is independent of specific volume for both gases. 

c. Develop expressions for vS for both the ideal and the Clausius gases that do not contain any derivatives other than Cand CP.

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