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Absolute Zero Physics 313 Professor Lee Carkner Lecture 15

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Exercise #14 Carnot Cycle Isothermal heat = work W = (1.5)(8.31)(700)ln(2X10 -3 /4X10 -4 ) Net work depends of efficiency = W/Q H = 0.6 Can get output heat from first law Q L = Q H - W = 14043-8426 = 5617 J

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Carnot and Temperature How are the heat exchanges related to the temperature? For ideal gas: Q H /Q L = T H /T L [(ln V 2 /V 3 )/ln V 4 /V 1 )] The volume term equals 1 (can relate V’s from the adiabatic processes)

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Temperature Scale Temperature can be related to the heat transfers of a Carnot engine Using the triple point of water Called the thermodynamic temperature Can make a “Carnot Thermometer” by running a Carnot engine at unknown T and T for triple point of water

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Absolute Zero If you lower T L, you lower Q L Defines absolute zero Absolute zero defined this is way is:

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Efficiency Can write the efficiency of a Carnot engine as: Increase the efficiency by increasing T H and decreasing T L ro For a Carnot refrigerator the coefficient of performance is:

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Entropy The limits on efficiency for engines and refrigerators are expressions of entropy Entropy represents a preferred direction for processes

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Heat and Temperature We saw that: If we include the signs of the heat: This is true for any Carnot cycle Any curve can be represented as the sum of many Carnot cycles

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Entropy Defined For any reversible cycle: The integral along any reversible (non- closed) path represents the change in entropy: dS = dQ/T

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Creating Entropy How might we change the entropy of a system Consider work done on a substance in contact with a heat reservoir at temperature T The ratio of work to the temperature of the reservoir is the entropy change Note:

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Ideal Gas Entropy To calculate entropy need expression for dQ dQ = C V dT +PdV S = C V (dT/T) + nR (dV/V) Similarly for: S = n c P (dT/T) - nR ln (P f /P i )

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T and S Heat can be expressed as: Heat is the area under the curve on a TS diagram

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The TS Diagram How are standard processes plotted on a TS diagram? Isotherm Adiabatic No entropy change, so vertical line

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Other Processes Isobar Curved line with slope: Isochor Curved line with slope:

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TS Diagram S T Isotherm Isentrope Isobar Isochor

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Entropy and Isotherms We write change in entropy as: If T is constant The change in entropy for an isothermal process depends only on the temperature and the total heat exchange

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