Chapter07

# Chapter07 - Conservation of Energy The equation of state...

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Conservation of Energy Conservation of Energy z The equation of state for gases and liquids is z The equation of state and the mass-and momentum- conservation principles provide five equations Mass: 1 scalar equation Momentum: 1 vector equation with 3 components State: 1 scalar equation z Unknowns for a Liquid: ρ , u , v , w , p – a total of 5 z Unknowns for a Gas: ρ , u , v , w , p , T – a total of 6 z If temperature variations are important, liquids also have 6 unknowns - energy conservation provides a sixth equation

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Thermodynamics Thermodynamics z The control-volume approach finds its origins in the science of thermodynamics, which deals with relations between heat and work z Thermodynamic Equilibrium Definition All transient motion ceases (mechanical equilibrium) All transient temperature changes cease (thermal equilibrium) All chemical activity ends (chemical equilibrium) z Strictly speaking, in thermodynamic equilibrium nothing is happening z We view a changing system as a succession of small steps from one equilibrium state to another, i.e., the process is quasi-static or quasi-steady
Thermodynamic Processes Thermodynamic Processes z Isovolumetric = constant volume z Isoenergetic = constant energy z Isothermal = constant temperature z Isentropic = constant entropy z Isobaric = constant pressure z Reversible Process = a process for which the state of a system and its surroundings can be restored…otherwise Irreversible z Adiabatic Process = no heat transfer between the system and the surroundings

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Equation of State and State Variables Equation of State and State Variables z If we deal with intensive properties, specifying any 3 determines the state of a substance… z Example: p = ρ RT for a perfect gas so that the state equation can be written as F(p, ρ ,T) = p – ρ RT = 0 z Any 3 state variables can be used The figure shows a p- υ -T diagram for water where υ = 1/ ρ is specific volume Note that volume increases at the temperature where water passes from liquid to solid state (ice)
First Law of Thermodynamics First Law of Thermodynamics z The First Law of Thermodynamics is z dE (a perfect differential) represents a change in the state of the system while δ Q and δ W (inexact differentials) are process and path dependent z For a reversible process δ W = pdV , so that z In terms of intensive variables… Change in system energy Heat added to system Work done by system on its surroundings

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Second Law of Thermodynamics Second Law of Thermodynamics - - 1 1 z The First Law of Thermodynamics says nothing about directionality An ice cube could get colder when placed on a hot surface Water could flow from the bottom to the top of a waterfall z We define entropy, s , to be a state variable such that z If δ q is the actual heat added, then δ q rev = heat added reversibly to the system
Second Law of Thermodynamics Second Law of Thermodynamics - - 2 2 z The Second Law of Thermodynamics says z The Second Law also states that the Clausius Inequality holds… z Since δ q

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## This note was uploaded on 10/12/2009 for the course AME 309 at USC.

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Chapter07 - Conservation of Energy The equation of state...

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