11. o 18% D ..ooo Sprint F 4:05 PM webassign.net (A) How many cycles of the heat
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11. o 18% D ..ooo Sprint F 4:05 PM webassign.net (A) How many cycles of the heat engine are necessary for it to do 6.40 104 Jof work? Display in New window (B) How much energy does the heat engine discharge as heat at the lower temperature as a result? CONCEPTUALIZE At the end of a complete cycle, the engine has returned to the same state in which it started, energy has been removed from the higher temperature reservoir, and a fraction of the energy determined by the efficiency is converted into work. The remainder of the energy has been released as heat to the lower temperature reservoir. CATEGORIZE The definition of the efficiency of the heat engine will be used to calculate how much of the input energy is transformed into useful work ANALYZE (A) How many cycles of the heat engine are necessary for it to do 6.40 x 104 Jof work? The efficiency of the heat engine is Solve this for IW and evaluate This value is the energy transferred by work in each cycle. The number of cycles needed to do the specified amount of work is then (B) How much energy does the heat engine discharge as heat at the lower temperature as a result? The total input energy in the n cycles is nQn and the part of it that is discharged at lower temperature is equal to e) n IQ. m 1 FINALIZE If the efficiency is increased, how does it affect the amount of energy that must be wasted by being discharged into the surroundings at lower temperature?Explanation / Answer
A)
Efficiency, e = work done/ heat supplied
work done is e*Heat supplied = 0.29*720 J = 208.8 J, This is for one cycle.
Number of cycles required be n, so n = 6.4*10^4/208.8 = 306.51
B)
For One cycle , the input energy is 720 J
For n cycles the energy is n*720 J
Part of energy that is discharged is (1-e)*n*720
= (1-0.29)*306.51*720 = 15.6 * 10^4 J
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