lecture24sp08

lecture24sp08 - Lecture 24 Heat Engines and the Second Law...

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Unformatted text preview: Lecture 24: Heat Engines and the Second Law of Thermodynamics 1 Chapter 18: The Internal Energy of a Gas In the example of Isothermal Expansion, the gas does work but stays at constant temperature. Normally when a gas expands, it will cool down, but in this case we have specified that the temperature remain constant. The only way that can happen is that heat is added to the gas. If you like, consider that the gas container in the figure is on some kind of stove top and heat is constantly being added as the volume expands. We can quantify this process by introducing the internal energy U int of a gas system. The thermodynamic variable U int is like the potential energy U int in mechanics. Its absolute value is not important, only changes in U int are physically significant. The variable U int can be changed by the gas doing work ( U int decreases), or heat being added to the gas ( U int increases). We write Δ U int = Δ Q- W The variable U int depends only on the temperature of the gas. As long as the temperature remains constant, then U int does not change 1 . Adiabatic Process In an isothermal expansion, heat Δ Q must be added to the gas to do work. At the other extreme is the adiabatic process where no heat is added to the expanding gas. In this case the internal energy U int must decrease by an amount equal to the work done by the expanding gas Q = 0 adiabatic process = ⇒ Δ U int =- W In an adiabatic process, the temperature of the gas must be lowered during an expansion. Generally, processes which happen so fast that there is no time for heat to be transferred (such as the compression stroke of a diesel engine, or the expansion of hot gases in a gasoline engine) are examples of adiabatic processes. Another example would be a well–insulated system such as the gas liquefaction in a refrigerator. 1 The textbook uses only the symbol U for internal energy. I have added a subscript “int” in order to emphasize that U int represents the internal energy in a thermodynamic system. Lecture 24: Heat Engines and the Second Law of Thermodynamics 2 Chapter 18: Heat Capacities for an Ideal Gas Heat Capacity Definitions and Relations The specific heat or heat capacity c of a solid or a liquid was defined according to how much heat Q was needed to raise a given mass m of the substance by one K (or one Celsius degree): Q = mc Δ T For an ideal gas, it is more useful to use either the 1) the molar heat capacity at constant volume called C V , or 2) the molar heat capacity at constant pressure called C P . We shall discover universal values for C V and a universal equation relating C P to C V . The molar heat capacity at constant volume C V for a gas is defined according to the differential amount of heat dQ needed increase n moles of a gas by an amount dT in Kelvin at constant volume of the gas: dQ = nC V dT 19 . 12 Since the volume of the gas does not change, then all of this heat increases the internal energy of the gas dU int = nC V dT The molar heat capacity at constant pressure...
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This note was uploaded on 04/18/2008 for the course PHYS 116a taught by Professor Maguire during the Spring '08 term at Vanderbilt.

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lecture24sp08 - Lecture 24 Heat Engines and the Second Law...

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