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Micro & Macro Descriptions of Internal Energy

Micro & Macro Descriptions of Internal Energy. P M V Subbarao Professor Mechanical Engineering Department. Important Form of Energy for Engineering Systems …. The Greatest Thermodynamic Relation. Internal Energy and Temperature. Substance A. Substance B. U B. U A.

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Micro & Macro Descriptions of Internal Energy

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  1. Micro & Macro Descriptions of Internal Energy P M V Subbarao Professor Mechanical Engineering Department Important Form of Energy for Engineering Systems …..

  2. The Greatest Thermodynamic Relation Internal Energy and Temperature Substance A Substance B UB UA If two substances are at same temperature, their microscopic translational kinetic energy must be same

  3. What is Temperature Really?

  4. What is Temperature Really? • Absolute Kelvin Temperature is proportional to average kinetic energy of atoms in a macroscopic system. • When atoms collide they tend on the average, to equalize kinetic energy spreads equally over all atoms. • This is called thermal equilibrium.

  5. Measurement of Energy • Macroscopic Energy: Easy to measure. • Microscopic Energy: Needs a detailed experiment. • Identify methods to measure economically.

  6. Measurement of Change in Internal Energy • First law for A control mass: Constant Volume Heating 1Q2 = U2 – U1 • Consider a homogeneous phase of a substance with constant composition. • Define Specific Heat: The amount of heat required per unit mass/mole to raise the temperature by one degree. • No change in other forms of energy, except internal energy.

  7. Constant Volume Specific Heat • The molar specific heat at constant volume is defined by • Based on microscopic theory, for a monatomic ideal gas, • Based on microscopic theory, for a polyatomic ideal gas,

  8. CV Specific Heats of Ideal Gases Experimental results

  9. Gas Constant Volume Heat Capacity CV(J/mol K) CV/R Ar 12.5 1.50 He 12.5 1.50 CO 20.7 2.49 H2 20.4 2.45 HCl 21.4 2.57 N2 20.6 2.49 NO 20.9 2.51 O2 21.1 2.54 Cl2 24.8 2.98 CO2 28.2 3.40 CS2 40.9 4.92 H2S 25.4 3.06 N2O 28.5 3.42 SO2 31.3 3.76

  10. What about any other process?

  11. General Process by A Control Mass • General (Polytropic) process of a control mass:

  12. Measurement of Changes during Constant Pressure Process • Constant pressure heating of a control mass: Constant Pressure Heating

  13. Constant Pressure Specific Heat • The molar specific heat at constant pressure is defined by • Using the first law of thermodynamics for a constant pressure process this can be put in the form • From a mono atomic ideal gas ( pV=nRT) under constant pressure conditions it can be seen that

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