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.

- Solutions
a. The equation for methane combustion is
. The enthalpy of combustion of methane is
.
. If gas at standard conditions is
and air is 21% oxygen, we get that there is
.

b. The volume of the boiler is
(will assume measurements had 2-3 sig figs if I wrote more carefully). At standard density, that gives a mass of water of
. The water receives
heat.

. The difference in temperature is
.
.

c. Steam evaporates until the pressure inside the boiler equals the vapor pressure of water at the current temperature. As heat continues to be added to the boiler, this pressure continues to increase.

d. This is where you can pull out the standard enthalpies from the steam tables (find a good one or two, learn how to read it, and add it your binder in case). According to Page 19 of this one, at 3.0MPa, saturated steam has a temperature of
and a standard enthalpy of
, whereas the water has a standard enthalpy of
.

For every kilogram of steam released, at least a kilogram of water must evaporate to take its place, so the furnace must match the difference in enthalpy, which is
.
. As a first order approximation, 11100kg will last
. If you wish to be more precise, as the last liquid water vaporizes, you still have
of pressurized steam when the valve would have to close to maintain pressure. Also according to the steam table, the steam takes up
, so
of water is still in the boiler as steam.

e. Now instead of replacing the change in enthalpy from
water into saturated steam, you additionally have to heat the replacement water up to that temperature from
, which has a standard enthalpy of
(correct me if I am significantly wrong to use the one at low pressure). Thus the total replacement enthalpy per kg of steam is
.

f. The intended answer was to preheat the feed water by running the pipe through the furnace exhaust, as there is excess heat and you are losing steam production to heat the water inside the boiler.

Not attempting g today.