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PHY-0002 (1)

140212 ch18_pt2.pdf

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Austin Napier

Notes added after lecture: •  In class we derived the molar specific heats for an ideal monatomic gas at constant pressure and at constant volume (see p. 621-623) and showed that: C P C =VR See Table 18-3 to compare with experiment. We can also look at the molar specific heats of diatomic and tri-atomic gases, using experimental data listed in Table 20-1 of Giancoli’s book “General Physics”. The next slide shows selected entries from that table. Note that the units are in (cal/mol.-K) instead of the usual (J/mol.-K). The ratio of the heat capacities is important because it determines the slope of adiabatic curves on the P-V diagram for the gas. This ratio is usually labeled γ (Greek letter “gamma”). For monatomic gases, γ = C /C = P V 5/3 = 1.67 , since CV=(3/2)R and C =P5/2)R. For diatomic gases, γ = (7/5) = 1.40, since C V(5/2)R and C =(P/2)R due to the two additional rotational degrees of freedom. For CO the value of γ is 1.30, since it is a tri-atomic molecule. 2 o Molar Heat Capacities of Gases at 15 C Gas CVcal/ CP CP-CV γ mol•K cal/mol•K cal/mol•K He 2.98 4.97 1.99 1.67 Ne 2.98 4.97 1.99 1.67 N 2 4.96 6.95 1.99 1.40 O 2 5.03 7.03 2.00 1.40 CO 6.80 8.83 2.03 1.30 2 The Laws of Thermodynamics Specific Heats, 2nd Law, Heat Engines, Carnot Cycle, Refrigerators Specific Heats for a Monatomic Ideal Gas: Constant Pressure, Constant Volume The P-V curve for an adiabat is given by where The Second Law of Thermodynamics We observe that heat always flows spontaneously from a warmer object to a cooler one, although the opposite would not violate the conservation of energy. This direction of heat flow is one of the ways of expressing the second law of thermodynamics: When objects of different temperatures are brought into thermal contact, the spontaneous flow of heat that results is always from the high temperature object to the low temperature object. Spontaneous heat flow never proceeds in the reverse direction. Heat Engines and the Carnot Cycle A heat engine is a device that converts heat into work. A classic example is the steam engine. Fuel heats the water; the vapor expands and does work against the piston; the vapor condenses back into water again and the cycle repeats. Heat Engines and the Carnot Cycle All heat engines have: • a high-temperature reservoir • a low-temperature reservoir • a cyclical engine These are illustrated schematically here. Heat Engines and the Carnot Cycle An amount of heat Q ishsupplied from the hot reservoir to the engine during each cycle. Of that heat, some appears as work, and the rest, Q , isc given off as waste heat to the cold reservoir. The efficiency is the fraction of the heat supplied to the engine that appears as work. Heat Engines and the Carnot Cycle The efficiency can also be written: In order for the engine to run, there must be a temperature difference; otherwise heat will not be transferred. Heat Engines and the Carnot Cycle The maximum-efficiency heat engine is described in Carnot’s theorem: If an engine operating between two constant- temperature reservoirs is to have maximum efficiency, it must be an engine in which all processe
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