work_to_heat_tra

# work_to_heat_tra - WORK-TO-HEAT TRANSDUCTION IN...

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WORK-TO-HEAT TRANSDUCTION IN THERMO-FLUID SYSTEMS E NERGY - BASED MODELING IS BUILT ON THERMODYNAMICS — the fundamental science of physical processes. T HERMODYNAMICS IS TO PHYSICAL SYSTEM DYNAMICS WHAT GEOMETRY IS TO MECHANICS . W HY SHOULD WE CARE ABOUT THERMAL PHENOMENA ? — they can profoundly influence dynamic behavior. Mod. Sim. Dyn. Syst. Work-to-heat transduction page 1

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EXAMPLE: A CLOSED BICYCLE PUMP air sealed outlet work in COMPRESSIBLE GAS ( AIR ) IN A CLOSED CONTAINER WITH VARIABLE VOLUME Compress the gas and it gets hot. When the gas is hotter than its surroundings the temperature gradient induces heat flow. Mod. Sim. Dyn. Syst. Work-to-heat transduction page 2
T HIS IS ANOTHER FORM OF ENERGY TRANSDUCTION — mechanical work to compress the gas is converted to heat. — governed by the first law. E NERGY TRANSDUCTION IS BILATERAL ( IT WORKS BOTH WAYS ) Heat the gas and its pressure increases. If the pressure moves the piston (to increase gas volume) mechanical work is done. Mod. Sim. Dyn. Syst. Work-to-heat transduction page 3

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Q UESTION : If you do work on the gas, can you get all of it back? (Answer: No — due to the second law.) Under what conditions is this energy “loss” significant? How do we integrate this behavior with our previous models? A T LEAST TWO DIFFERENT PHENOMENA ARE INVOLVED : energy storage power dissipation Mod. Sim. Dyn. Syst. Work-to-heat transduction page 4
ENERGY STORAGE IN A COMPRESSIBLE GAS E NERGY IS ADDED TO ( OR TAKEN FROM ) THE GAS IN TWO FORMS — mechanical work or heat M ODEL THIS AS A MULTIPORT ENERGY STORAGE ELEMENT — but of what kind? Mod. Sim. Dyn. Syst. Work-to-heat transduction page 5

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A RELEVANT STATEMENT OF THE FIRST LAW: U = Q W U: internal energy of the gas Q: heat added to the gas W: work done by expansion of the gas (Notation and sign convention are standard for engineering thermodynamics.) A PPLY THIS ON AN INSTANT - BY - INSTANT BASIS USING ITS DIFFERENTIAL FORM . dU = dQ – dW Mod. Sim. Dyn. Syst. Work-to-heat transduction page 6
ON THE MECHANICAL SIDE: dW = PdV P: pressure V: volume T HE GAS BEHAVES AS A CAPACITOR ON THE MECHANICAL SIDE work is a form of energy pressure is an effort volume is a displacement Mod. Sim. Dyn. Syst. Work-to-heat transduction page 7

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A COMMENT ON SIGN CONVENTION P OSITIVE WORK COMPRESSES THE GAS — a negative volume change, –dV. dW = P(–dV)
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work_to_heat_tra - WORK-TO-HEAT TRANSDUCTION IN...

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