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Unformatted text preview: - 1 - Physics 2213 HW #3 Solutions Fall 2008 18.41 [Heat Capacities] 5 /2 V C R = for a diatomic ideal gas and 3 /2 V C R = for a monatomic ideal gas. (a) ( 29 5 2 V Q nC T n R T = = ( 29 5 2 (2.5 mol) (8.3145 J/mol K)(30.0 K) 1560 J Q = = (b) ( 29 3 2 V Q nC T n R T = = ( 29 3 2 (2.5 mol) (8.3145 J/mol K)(30.0 K) 935 J Q = = More heat is required for the diatomic gas; not all the heat that goes into the gas appears as translational kinetic energy, some goes into energy of the internal motion of the molecules (rotations). 19.23 [Auto Engine R&D] For constant volume, V Q nC T = , whereas for constant pressure, p Q nC T = . For nitrogen, 20.76 J/mol K V C = and 29.07 J/mol K p C = . (a) The pV-diagram is sketched in figure (a) below. 645 J 167.9 K (0.185 mol)(20.76 J mol K) V Q T nC = = = and 948 K . T = (b) The pV-diagram is sketched in figure (b) below. 645 J 119.9 K (0.185 mol)(29.07 J mol K) p Q T nC = = = and 900 K . T = At constant pressure some of the heat energy added to the gas leaves the gas as expansion work and the internal energy change is less than if the same amount of heat energy is added at constant volume. T is proportional to . U 19.34 [Ferrari Engine] (a) In the process the pressure increases and the volume decreases. The pV-diagram is sketched below. - 2 - (b) For an adiabatic process for an ideal gas 1 1 1 1 2 2 , TV T V -- = 1 1 2 2 , p V...
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