HW_wk3_solutions_06 - Chem_2R03 HW3_Solutions All gases are...

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Chem_2R03 HW3_Solutions Sept 28 2006 All gases are assumed to be ideal unless otherwise specified 1. When we are interested in biological energy resources and metabolism, we need to know, among other things, the work that an organism has to do to carry out the normal activities of being alive. How much metabolic energy must a bird of mass 200 g exert to fly to a height of 20 m? Neglect all losses due to friction, physiological imperfection, and the acquisition of kinetic energy. Solutions: ( 29 ( 29 ( 29 -2 1 kg 20 m 200 g 9.80 m s 1000 g 39 J w hmg w w = = = 2. The heat capacity of air is much smaller than that of water, and relatively modest amounts of heat are needed to change its temperature. This is one of the reasons why desert regions, though very hot during the day, are bitterly cold at night. The heat capacity of air at room temperature (298K) and pressure (1 atm) is approximately 21 J K -1 mol -1 . How much energy is required to raise the temperature of a room of dimensions 5.5 m × 6.5 m × 3.0 m by 10 o C? Solutions: 3 25 . 107 0 . 3 5 . 6 5 . 5 m m m m V = × × = mol K K mol J m Pa RT pV n 3 1 1 3 5 10 39 . 4 298 315 . 8 25 . 107 10 01325 . 1 × = × × × = = - - 3 1 1 5 4.39 10 21 10 9.2 10 m q C T nC T mol J K mol K J - - = ∆= ∆= = ��״ 3. The molar heat capacity of water is 75.3 J K -1 mol -1 . How much energy (heat) is needed to heat up by 40ºC 250 g of water for a cup of coffee? Solutions: ( 29 ( 29 ( 29 ( 29 ( 29 -1 -1 -1 -1 250 g 13.9 mol 2 1.0079 g mol 15.999 g mol 1 kJ 13.9 mol 75.3 J K mol 40 K 1000 J 42 kJ m m q C T C C n q nC T m n M n q q = = = = = = + = = 1
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Chem_2R03 HW3_Solutions Sept 28 2006 4. A sample of serum at a mass 25 g is cooled from 290 K to 275 K at constant pressure by the extraction of 1.2 kJ of energy as heat. Calculate q and ΔH and estimate the specific heat capacity of the sample.
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