Problem 1:
If one were to roll a tetrahedral (4-sided) die twelve times, show that the most likely outcome would be to get three rolls of each number (i.e. three 1's, three 2's, three 3's, and three 4's). Show your work.
problem 2:
A 300 hp (223.71 kW) truck engine consumes fuel at a rate of 10.567 gallons every hour (40 L/h). The fuel has a heating value of 45 MJ/kg and a density of 0.8 g/cm3. What is the thermal efficiency of this engine?
problem 3:
A 200 MW power plant creates steam by burning coal with a heating value of 25,000 kJ/kg. The coal-burning furnace requires 12 kg of air for every 1.0 kg of coal burned. If the power plant has an overall thermal efficiency of 32%, determine (a) the amount of coal consumed during one day in kg and (b) the mass flow rate of air through the furnace in kg/s.