Flow of Fluids—Energy and Momentum Relationships

Calculate the ideal available energy produced by the discharge to atmosphere through a nozzle of air stored in a cylinder of capacity 0.1 at a pressure of 5 MN/m. The initial temperature of the air is 290 K and the ratio of the specific heats is 1.4. 

Obtain expressions for the variation of (a) internal energy with change of volume, 

The key to this solution lies in the fact that the operation involved is an irreversible expansion. Taking C as constant between T and T2, AU = — W = nCv(T2 — Ti) where n is the kmol of gas and T2 and Ti are the final and initial temperatures, then for a constant pressure process, the work done, assuming the ideal gas laws apply, is given by  

Equating these expressions for W gives —Cv(T2 — Ti) = P2 In this example  

Compressed gas is distributed from a works in cylinders which are filled to a pressure P by connecting them to a large reservoir of gas which remains at a steady pressure P and temperature P. If the small cylinders are initially at a temperature P and pressure Po, what is the final temperature of the gas in the cylinders if heat losses can be neglected and if the compression can be regarded as reversible Assume that the ideal gas laws are applicable. 

Obtain expressions for the variation of (a) internal energy with change of volume, (b) internal energy with change of pressure, and (c) enthalpy with change of pressure, all at constant temperature, for a gas whose equation of state is given by van der Waals law. 

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FLOW OF FLUIDS —ENERGY AND MOMENTUM RELATIONSHIPS Putting P = Pcx) = atmospheric pressure ... 

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