#$&* course PHY 202 009. `query 9 was submitted 16 Jun 2011 around 6:00 PM. 009. `query 9*********************************************
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Given Solution: The maximum possible efficiency is (T_h - T_c) / T_h, where T_h and T_c are the absolute max and min operating temperatures. T_h is (580 + 273)K = 853 K and T_c is (380 + 273) K = 653 K, so the maximum theoretical efficiency is max efficiency = (T_h - T_c) / T_h = (853 K - 653 K) / (853 K) = .23, approx. This means that the work done by this engine will be not greater than about 23% of the thermal energy that goes into it. Your Self-Critique: ok Your Self-Critique Rating: 3 ********************************************* Question: query gen phy problem 15.26 source 550 C -> Carnot eff. 28%; source temp for Carnot eff. 35%? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your Solution: According to Carnot, for an ideal reversible engine, the heat input to the engine be at temperature T_h, and the heat output be at a temperature T_c. Carnot efficiency is eff = (Th - Tc) / Th. Solving this for Tc we multiply both sides by Th to get eff * Th = Th - Tc so that Tc = Th - eff * Th = Th ( 1 - eff). All temperatures must be absolute (Kelvin scale) (adding 273 C to the Celsius temperature) At an inlet temperature of 550 C, the Carnot engine has an efficiency of 28%. From that data we can find the exhaust temperature of the engine T_c. If T_h = 550 C = 823 K and efficiency is 30% then we have T_c = 823 K * ( 1 - 0.28) = 592 K. Now we want Carnot efficiency to be 35% for this T_c. We solve eff = (T_h - T_c) / T_h for T_h: T_c we multiply both sides by T_h to get eff * T_h = T_h - T_c so that eff * T_h - T_h = -T_c and T_c = T_h - eff * T_h or T_c = T_h ( 1 - eff) and T_h = T_c / (1 - eff). If T_c = 576 K and eff = 0.35 we get T_h = 592 K / ( 1 - 0.35 ) = 592 C / .6 = 912 K This is (912 - 273) C = 639 C confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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: ok Your Self-Critique Rating: 3 " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!