Chemistry 231 Tutorial Session 3 G. Marangoni Date: Friday, October 24, 2008. The following questions will be answered on the tutorial session. 1. Calculate the efficiency of the following process. a. A Carnot engine operating between 520K and 298 K. b. A Carnot refrigerator operating between -5C and 30C. c. An air conditioning system operating between 5C and 32C. d. A heat pump operating between -10C and 22C. 2. A Carnot engine, containing 497 kPa of an ideal gas (Cv,m = 5/2 R, V1 = 1.50 L) as the working fluid, operates between 640 K and 300 K. Assuming that the volume on the downstroke of the engine is 4.0L, calculate q, w, U and H for each step in the process. Please answer the following questions. Answers will be posted on the website. 3. An automobile engine operates between 600C and 298 K. The enthalpy of combustion of iso-octane (gasoline) is 2.23 kJ/g and its density is 0.78 g/mL. a. Calculate the Carnot efficiency of an engine. b. Calculate the overall efficiency of the engine if it 40% of its Carnot efficiency. c. For the real auto engine, calculate the amount of gasoline (in L/h) required to do 905W of work. 4. The Chalk Point Maryland Power station has a gross electrical generating capacity of 710 MW. At a steam pressure of 3600 psi, the outlet temperature at the super-exchanger is 540C, and the condensate temperature is 30C. a. Calculate the Carnot efficiency of the generating station. b. If the boiler efficiency is 91.4% and the turbine efficiency is rated at 46.7% (note this includes the Carnot efficiency and mechanical losses), and the generator is 98.4%, what is the overall efficiency of the plant? c. One of the coal burning units in this plant produces 355 MW of power. How many metric tons of coal are required per hour are required to fuel the unit (note – the heat of combustion of coal is 29.0 MJ/Kg). d. How much heat is rejected to the cold temperature reservoir per minute? e. Assume that 960 000 L of water pass through the condenser in a minute. Calculate the temperature rise in the water (note for H2O, Cp = 4.184 J/(g K)). Answers 1. a. For a Carnot engine Tc Th 298K 1 520K C 1 0.427 b. For a Carnot refrigerator Tc r Th Tc 268K 303 268K 7.66 c. Treat the air conditioning systems as a Carnot refrigerator r Tc Th Tc 278K 305 278K 10.3 d. For a Carnot heat pump hp Th Th Tc 295K 295 263K 9.22 2. For the Carnot engine operating between 640 K and 300 K Tc Th 300K 1 640K C 1 0.531 Step 1 - Isothermal, reversible expansion U1 = H1 = 0; q1 = -w1. V w 1 nRT ln 2 V 1 J 4.0L x 640Kx ln Kmole 1.5L 731J q 1 731J 0.140molex 8.314 Step 2 – Ideal gas, adiabatic, reversible expansion U2 = w2; q2 = 0. U2 = nCv,mT = 0.140 mole x 5/2 x 8.314 J/(K mole) x (-340 K) = -990 J = q2 H2 = nCp,mT = 0.140 mole x 7/2 x 8.314 J/(K mole) x (-340 K) = -1385 J Step 3 - Isothermal, reversible compression U3 = H3 = 0; q3 = -w3. V w 3 nRT ln 2 V 1 J 1.50L 0.140molex 8.314 x 300Kx ln Kmole 4.00L 342J q 3 342J Step 4 – Ideal gas, adiabatic, reversible compression U4 = w4; q4 = 0. U4 = nCv,mT = 0.140 mole x 5/2 x 8.314 J/(K mole) x (340 K) = +990 J = q4 H4 = nCp,mT = 0.140 mole x 7/2 x 8.314 J/(K mole) x (340 K) = +1385 J Note for the cycle qcycle = q1 + q2 + q3 + q4 = 731 J-342 J = 389 J wcycle = -qcycle = -389 J Note w cy cle Tc Th q1 389J 731J C 1 0.532 3. Calculate the efficiency as if the engine operate as a Carnot Engine a. For a Carnot engine T C 1 c Th 298 K 873K 0.656 1 b. For a real engine with an efficiency 40% of that of the Carnot engine C C 0.40 0.656 0.40 0.263 c. For the real engine, in order to do 905 W of work. w C cycle q1 905 J s 1 0.263 q1 905 J s 1 0.263 3435 J s 1 q1 C wcycle q1 905 J s 1 0.263 q1 905 J s 1 0.263 3435 J s 1 q1 For one hour – the heat required is 1.237 x 107 J, or 1.237 x 104 kJ The mass of fuel required. 1.237 104 kJ g of fuel 2.23kJ g 1 5.543 103 g of fuel 5.543 103 g 0.78 g mL1 7109 mL 7.11L mL of fuel 4. Calculate the efficiency of the boiler system a. Carnot efficiency T C 1 c Th 303K 813K 0.627 62.7% 1 b. To obtain the overall efficiency, we have to multiply turbine efficiency (which is a composite of the ideal, Carnot efficiency and frictional and other mechanical losses) by the boiler and the generator efficiency overall C B G 0.467 0.914 0.984 0.467 0.899 0.420 42.0% c. To produce 355MW of power. overall 0.420 wcycle q1 355 106 J s 1 q1 355 106 J s 1 0.420 845 106 J s 1 The amount of coal per second is Kg coal = 845 MJ s-1 / 291 MJ kg-1 = 29.1 kg s-1 q1 For one hour – the amount required is 29.1 kg s-1 x 3600 s = 105 Mg h-1 = 105 metric tonnes d. Note q1 q3 wcycle q3 q1 wcycle 845MJ 355MJ q3 490 MJ 4.90 108 J e. Note – for one minute q3 490MJ s 1 4.90 108 J s 1 60 s 2.94 1010 J 96000 L 9.60 108 g q3 T mH 2O 4.184 J g 1K 1 2.94 1010 J 7.2 K 7.2 oC 8 1 1 9.60 10 g 4.184 J g K