This may be more than anything I personally remember ever seeing on a thermo test, but yet still potentially a feasible test question (for C division at least), and I have recently developed an interest in boilers.
A sealed, perfectly insulated boiler is a cylinder with the (interior) dimensions of 1m in radius, 5m height and is 70% full of water at 25C. Assume ambient pressure of 1atm and ignore the heat capacity of the boiler. A furnace burns methane at a rate of 15MW and transfers 60% of the heat to the boiler.
a. What is the minimum stoichiometric air flow to the furnace in m^3/minute?
b. How fast will the furnace initially heat in degrees Celsius per minute? When will it reach boiling point?
c. Describe what happens inside the boiler as heat continues to be added.
d. Once the boiler reaches a pressure of 3MPa (absolute), a valve is kept opened such to maintain a constant pressure. Once most of the air is removed from the boiler, determine the following: the temperature of the boiler, the outflow rate of steam in kg/minute, an estimate of the time before the boiler runs dry (you may ignore factors like changing steam volume and water evaporated to reach steady state).
e. Feed water is now fed into the boiler at 20C and an equilibrium state with a water level of 50% is reached. Determine the new steam outflow rate.
f. What else can be done for the boiler to produce more steam without increasing the furnace output?
g. (Extra) The boiler fails catastrophically under full operating conditions. Estimate the size of the resulting steam cloud, neglecting the work done on the (former) boiler and the immediate surroundings.