#$&* course Phy 232 9/13 09. `query 9
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Given Solution: The maximum possible efficiency is (T_h - T_c) / T_h, where T_h and T_c are the absolute max and min operating temperatures. T_h is (580 + 273)K = 853 K and T_c is (380 + 273) K = 653 K, so the maximum theoretical efficiency is max efficiency = (T_h - T_c) / T_h = (853 K - 653 K) / (853 K) = .23, approx. This means that the work done by this engine will be not greater than about 23% of the thermal energy that goes into it. Your Self-Critique: Your Self-Critique rating #$&* ********************************************* Question: query gen phy problem 15.26 source 550 C -> Carnot eff. 28%; source temp for Carnot eff. 35%? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your Solution: confidence rating #$&* ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** Carnot efficiency is eff = (Th - Tc) / Th. Solving this for Tc we multiply both sides by Th to get eff * Th = Th - Tc so that Tc = Th - eff * Th = Th ( 1 - eff). We note that all temperatures must be absolute so we need to work with the Kelvin scale (adding 273 C to the Celsius temperature to get the Kelvin temperature) If Th = 550 C = 823 K and efficiency is 30% then we have Tc =823 K * ( 1 - .28) = 592 K. Now we want Carnot efficiency to be 35% for this Tc. We solve eff = (Th - Tc) / Th for Th: Tc we multiply both sides by Th to get eff * Th = Th - Tc so that eff * Th - Th = -Tc and Tc = Th - eff * Th or Tc = Th ( 1 - eff) and Th = Tc / (1 - eff). If Tc = 576 K and eff = .35 we get Th = 592 K / ( 1 - .35 ) = 592 C / .6 = 912 K, approx. This is (912 - 273) C = 639 C. ** Your Self-Critique: Your Self-Critique rating #$&* ********************************************* Question: univ phy problem 20.45 11th edition 20.44 (18.40 10th edition) ocean thermal energy conversion 6 C to 27 C At 210 kW, what is the rate of extraction of thermal energy from the warm water and the rate of absorption by the cold water? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your Solution: First we have to find the efficency of the system: e= W/Qh=1-absolute value (Qc/Qh)=1-(6+273 K/27+273 )=7% To find the rate of extraction we can use the equation e= W/Qh=(W/t)/(Qh/t)=P/(Qh/t) Because P=W/t Rearrange to Qh/t=P/e=210kw/.07=3MW. Since W=Qh+Qc, The energy absorbed by the cold water is 3MW-210KW=2.8MW The water leaves the cycle at 10 degrees according to my book. This is a 4 degree temp change for the cold water.To figure out how muc water passes through the system per hour use Q=mcdT rearrange to Q/m=cdT, multiply both sides by ""1"": (t/t)(Q/m)=cdT x1 and rearrange to m/t= (Qc/t)/cdT=2.8 x 10^6 W/(4190J/(kgxK) x 4K) x 3600 sec/hr=600000 kg/hr or 600000L/hr confidence rating #$&* ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** work done / thermal energy required = .07 so thermal energy required = work done / .07. Translating directly to power, thermal energy must be extracted at rate 210 kW / .07 = 3,000 kW. The cold water absorbs what's left after the 210 kW go into work, or 2,790 kW. Each liter supplies 4186 J for every degree, or about 80 kJ for the 19 deg net temp change. Needing 3,000 kJ/sec this requires about 40 liters / sec, or well over a hundred thousand liters / hour (a hundred cubic meters per hour). Comment from student: To be honest, I was surprised the efficiency was so low. Efficiency is low but the energy is cheap and environmental impact in the deep ocean can be negligible so the process can be economical. ** Your Self-Critique:I think I went a little more in depth than the given solution. Also , the given solution used the dT of the warm water to calculate the flow of water, but I used the dT of the cold water. Maybe this is because I have the 12ed of the book, because my answer matched the one given in my book *&$*&$ Your Self-Critique rating #$&*10