Department of Mechanical Engineering ME 322 – Mechanical Engineering Thermodynamics Lecture 17 Unsteady State (Transient) Analysis

What is a Transient Process? 2 A transient process occurs whenever the time derivative related to the system gain (or loss) is not zero... Filling a tank Emptying a tank

Department of Mechanical Engineering ME 322 – Mechanical Engineering Thermodynamics Example – Problem

Example – Filling a Tank 4 Given: Filling a rigid tank with oxygen Find: The heat transfer required to fill the tank isothermally Use the ideal gas model for oxygen properties

Example 5 The First Law for the system is,

Example 6 So far, the following expression for the system has been developed, Some observations... The problem asks for the heat transferred (total energy) but the First Law has a heat transfer rate How do I know what the mass flow rate into the tank is? Is this a constant value? How do I represent the derivative on the RHS?

Example 7 The mass flow rate in is contained in the conservation of mass, Making this substitution into the First Law, Multiply both sides by dt,

Example 8 This equation can be integrated over the time of the filling process,

Example 9 Substituting and rearranging, The oxygen is being modeled as an ideal gas. Therefore, Substitution into the First Law results in,

Example 10 Finally, doing the calculations... What is T i ? There is a valve between the tank and the line. However, we know that a valve is isenthalpic. Since enthalpy is constant and the substance is being modeled as an ideal gas, the throttling process is also isothermal. Therefore, The heat transfer is from the oxygen (the assumed direction was wrong)