# 1b-r - Conservation of Energy Chapter One Section 1.3...

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Conservation of Energy Conservation of Energy Chapter One Chapter One Section 1.3 Section 1.3

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Alternative Formulations Alternative Formulations Time Basis: At an instant or Over a time interval Type of System: Control volume Control surface An important tool in heat transfer analysis, often providing the basis for determining the temperature of a system. CONSERVATION OF ENERGY (FIRST LAW OF THERMODYNAMICS)
At an Instant of Time: Note representation of system by a control surface (dashed line) at the boundaries. Surface Phenomena , energy transfer across the control su : rate of thermal and/or mechanical due to heat transfer, fluid flow and/or wor rfa k i c nteract io . e ns in out E E g g Volumetric Phenomena : rate of due to conversion from another enegy form (e.g., electrical, nuclear, or chemical); energy conversion proc thermal ener ess occurs w gy generatio ithin the sy e n m. st g E g energy storage in the system : rate of change . of st E g Conservation of Energy in out g st dE st dt E E E E - + = g g g g (1.11c) Each term has units of J/s or W. APPLICATION TO A CONTROL VOLUME Over a Time Interval Each term has units of J. in out g st E E E E - + = (1.11b) CV at an Instant and over a Time Interval

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At an instant t dU q W dt - = g Special Cases (Linkages to Thermodynamics) (i) Transient Process for a Closed System of Mass ( M) Assuming Heat Transfer to the System (Inflow) and Work Done by the System (Outflow). Over a time interval tot st Q E W - = ∆ (1.11a) Closed System For negligible changes in potential or kinetic energy t Q W U - = ∆ Internal thermal energy
Example 1.3: Application to thermal response of a conductor with Ohmic heating (generation): Involves change in thermal energy and for an incompressible substance. t dU dT Mc dt dt = Heat transfer is from the conductor (negative ) q Generation may be viewed as electrical work done on the system (negative ) W g Example 1.3

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Example 1.4: Application to isothermal solid-liquid phase change in a container: Latent Heat of Fusion t 1at sf U U M = ∆ = h Example 1.4
(i) Steady State for Flow through an Open System without Phase Change or Generation: ( 29 flow o w rk pv ( 29 enthalp y t u pv i + ≡ → ( 29 ideal gas constant specific h For an w eat ith : in out p in

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## This note was uploaded on 02/21/2009 for the course MAE 310 taught by Professor Kuznetsov during the Spring '08 term at N.C. State.

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1b-r - Conservation of Energy Chapter One Section 1.3...

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