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The 1 st Law of Thermodynamics and Simple Systems

The 1 st Law of Thermodynamics and Simple Systems. Calculating Internal energy. Since the Internal Energy of a gas is the sum of the E K of it’s molecules Kinetic theory And the Average E K of a molecule is found by the equation E K Average = (3/2)kT

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The 1 st Law of Thermodynamics and Simple Systems

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  1. The 1st Law of Thermodynamics and Simple Systems

  2. Calculating Internal energy • Since the Internal Energy of a gas is the sum of the EK of it’s molecules • Kinetic theory • And the Average EK of a molecule is found by the equation EK Average = (3/2)kT • The total internal energy must be sum of all the molecules energy • U = (3/2)NkT • U = (3/2)nRT

  3. What the 1st law really is • Since thermodynamics is the study on how thermal energy is transferred and transformed into other energies this first law must relate to energy. • We have only one law for energy… • The Conservation of Energy • So the 1st law of thermodynamics must be a restatement of the conservation of energy. Only with a specific focus.

  4. The First Law of Thermodynamics • Because we are interested in the energy transformations within a gas the conservation of energy must be focuses on that. • The 1st Law of Thermodynamics: The change in a gases internal energy must equal the Energy that flows into the gas (Heat) minus the Energy the gas uses to expand (Work) • Change gas’s internal Energy = Heat – Workby gas • DU = Q – Wby gas

  5. Going with the flow • It is important to always remember that both Heat on work are energies that flow into and out of the gas. • They are not properties of the gas itself • Internal energy however is apart of the gas and is one of the gas’s properties. • The change in internal energy then is a change in one of the gas’s properties (related to temperature)

  6. Visualizing the 1st law W Q DU = Q -W

  7. Types of thermal Systems • There are 4 simple systems for a heated gas: • Isobaric • Isovolumetric/Isochoric • Isothermal • Adiabatic

  8. Isobaric systems • Is a system where a gas expands, or contracts, in a way that its pressure remains constant. Pressure Pressure Expanding Compressing Volume Volume

  9. W = F//D D D DV = AD DV W = Area Pressure Volume Calculating Work for an Isobaric system F// = PA W = PAD W = PDV

  10. Is volumetric • This is when a gas is placed in a container that will not change it’s size. • Since the gas will not expand or contract there can be no work done by, or on, the gas • W = 0 J Pressure No Area Volume

  11. Isothermal • This is a very slow process which allows the gas to expand, or contract, so that it’s Temperature is constant. • This means that the gas’s internal energy is a constant (U = [3/2]NRT) • This also means that PV is a constant (PV = nRT)

  12. PV graph for Isothermal P1 Graph function: xy = c Pressure P2 Area = work V2 V1 Volume P1V1 = P2V2

  13. T2 Pressure T1 Volume T2 > T1

  14. Adiabatic Systems • Adiabatic systems when a gas expands, or contracts, very quickly. • Popping a balloon • Ignition of a sparkplug • Firing a single shoot from a gun • There is no time for any heat to flow in or out of the gas. • Q = 0 Joules • In this case any work done must change the internal energy. (PV is not constant.)

  15. P1V1 =P2V2 PV graph for Adiabatic P1 Pressure P2 Area = work V2 V1 Volume

  16. Table of simple systems

  17. Stating the DU in terms of PV • It is sometime easier to solve problems when we think of the change of internal energy in terms of PV rather than T. • Particular when working with a PV graph U = (3/2)NRT PV = NRT U = (3/2)PV DU = (3/2)[PfVf – PiVi]

  18. Viewing a Simple Engine Provides Heat (Energy) for the engine to work Hot Reservoir QH Gas Chamber W Output Receives the Mechanical work done QC W = QH - QC Cold Reservoir Receives all the wasted exhaust of engine

  19. Efficiency • Efficiency = Workout/Workin • Efficiency = Workout/QH • Efficiency = (QH – QC)/QH • Efficiency = 1 – (QC/QH)

  20. Carnot Efficiency • No engine can be 100% Efficient (even if it is an ideal engine). • You need to use some energy to reset you engine for the next cycle. • So this leads to the question:” If the maximum efficiency is not 100%, how can I tell how good is the efficiency of my engine?” • A French scientist name Sadi Carnot found a way of calculating the ideal (maximum) efficieny for a given engine. • No engine can achieve it’s ideal efficiency

  21. Carnot efficiency • Carnot found that the ideal Efficiency depends to the two absolute temperatures (Temperature measured in Kelvin) of the two Reservoir • EfficiencyCarnot = 1 – (TC/TH)

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