Kinetic Energy for a mass (m) at a velocity (V) (an Extensive Property) Frequently, one is interested in the change of KE from State 1 to State 2:

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1 Kinetic Energy for a mass (m) at a velocity (V) (an Extensive Property) Frequently, one is interested in the change of KE from State 1 to State 2: Potential Energy for a mass (m) in a gravational potential field (g) at a height z (an Extensive Property) Frequently, one is interested in the change of PE from State 1 to State 2: Internal Energy (U): A measure of energy at a macroscopic level due to the molecular translation, vibration, rotation (an Extensive Property). Internal Energy can also be expressed as an intensive property u=u/m (internal energy per unit mass). 3 of 59 9/2/13 5:29 PM

2 Frequently, internal energy is presented in tables, such as Table A-4 for superheated water vapor. The Design and Analysis of many engineering systems requires thermodynamics (in addition to fluid mechanics, heat transfer, structural analysis, etc.) Consider a Simple Power System. Thermodynamics establishes the limits on the Maximum Power Out (Work Out) for a given Qin for a particular system of interest. 5 of 59 9/2/13 5:29 PM

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9 ****************************** We rarely use the Compressed Liquid tables. Generally, the values are very close to those in the saturated tables at the given temperature. That is, changing the pressure of a liquid does not significantly change the state properties (other than pressure). 23 of 59 9/2/13 5:29 PM

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A video game style song of thermodynamics http://www.wiziq.

21 A video game style song of thermodynamics 34 of 59 9/4/13 11:29 AM

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29 You will need to analyze the integral of PdV in order to estimate the work associated with volume expansions/compressions. So, for polytropic situations: pv n = constant, then 42 of 59 9/2/13 5:29 PM

30 But, most gas situations will use Tables that have combined the Internal Energy (U) with the pv and a thermodynamic term (Enthalpy, H or h) is documented. That is: H = U + pv h = u + pv (more on this when we reach Chapter 3) 43 of 59 9/2/13 5:29 PM

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Well-balanced schemes for the Euler equations with gravitation

Well-balanced schemes for the Euler equations with gravitation Roger Käppeli Joint work with S. Mishra Outline Introduction Well-balanced scheme for HydroStatic Equilibrium (HSE) First order Second order