P2213_HW04_solns_Fall2008

P2213_HW04_solns_Fall2008 - 1 Physics 2213 HW#4 —...

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Unformatted text preview: - 1 - Physics 2213 HW #4 — Solutions Fall 2008 20.3 [Gasoline Engine] We have 3700 W W = + for work and H 16,100 J Q = + for positive heat flowing into the system. (a) H work output 3700 J 0.23 23% . heat energy input 16,100 J W e Q = = = = = (b) H C W Q Q Q = =- Heat discarded is C H 16,100 J 3700 J 12, 400 J . Q Q W =- =- = (c) H Q is supplied by burning fuel; H c Q mL = where c L is the heat of combustion. H 4 c 16,100 J 0.350 g . 4.60 10 J/g Q m L = = = × (d) 3700 J W = per cycle In 1.0 s t = the engine goes through 60.0 cycles. / 60.0(3700 J)/1.00 s 222 kW P W t = = = 5 (2.22 10 W)(1 hp/746 W) 298 hp P = × = Note: In one cycle tot C H 3700 J. Q Q Q = + = This equals tot W for one cycle from energy conservation. 20.12 [A Freezer] Coefficient of performance of a refrigerator C Q K W = , and H C Q Q W = + from energy conservation. (a) ice ice f w w . Q mc T mL mc T = ∆- + ∆ For water, w 4190 J/kg K c = ⋅ and 5 f 3.34 10 J/kg. L = × For ice, ice 2010 J/kg K. c = ⋅ 5 5 (1.80 kg)([2010 J/kg K][ 5.0 C ] 3.34 10 J/kg [4190 J/kg K][ 25.0 C ]) 8.08 10 J Q = ⋅-- × + ⋅- = - × ° ° 5 8.08 10 J . Q = - × Q is negative for the water since heat is removed from it. (b) 5 C 8.08 10 J. Q = × 5 C 5 8.08 10 J 3.37 10 J . 2.40 Q W K × = = = × (c) 5 5 6 H 8.08 10 J 3.37 10 J 1.14 10 J . Q = × + × = × For this device, C Q and H 0. Q < More heat is rejected to the room than is removed from the water. - 2 - 20.23 [Maximum Output] The power output is given by cycle W P t = ∆ , where W is work done over time cycle t ∆ of each cycle. The theoretical maximum efficiency is that of a Carnot cycle, C Carnot H 1 T e T = - . Using the definition of efficiency, H Carnot W e e Q = = , we find 1 C H H cycle T Q P T t =- ∆ . In this problem we are given 4 H 1.50 10 J Q = × , C 350 K T = , and H 650 K T = . Time it takes for one cycle is 60 s / 240 0.25 s cycle t ∆ = = . To convert power from Watts into horsepower, we will use the fact that 1 hp 746 W = ....
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P2213_HW04_solns_Fall2008 - 1 Physics 2213 HW#4 —...

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