what happens if pressure drops suddenly without droping in the temperature in the boiler?
Really depends on the temperature. But for any liquid the following will happen. Almost instantly enough of the liquid will evaporate to drop the boiling point of the liquid down to a temperature that corresponds to the boiling point at the new lower pressure. Flashing is what I think they call that. In boilers its a bad situation. Since in some cases the water inside the boiler fizzes off like a shaken up can of soda. The level indicators show the boiler full of water but its not. Depending on the type of boiler and if its under fire the tubes could be damaged by being over heated.
Boiling fastens thereby creating more fumes due to the scales and sludges and hence results in boiler explosion.
because PV=constant in your application, as pressure drop suddenly the volume may increase suddenly and it may cause to exploid the boiler.
In the real world, you probably developed a leak, the outside temperature dropped to greatly increase the load, the blowdown valve was not properly closed, or some other source of big increase in load demand.
None of the above is correct. If the pressure is reduced, the boiler will not explode. It is excess pressure that causes the boiler to explode. However, assuming that you are boiling a liquid assumes that there is heat (energy) being added to the boiler to facilitate the phase change. If you reduce the pressure, you will accelerate the boiling (the rate of phase change). Once the liquid is completed changed to vapor phase, the temperature will begin to rise (the temperature was being held at the boiling point of the liquid phase @ the given vessel pressure as long as there was fluid in the vessel). If the pressure reduction was due to a leak, the only affect is the rise in temperature and corresponding expansion of gas volume (per the PVT relationship for gas), which will leak out the opening causing the initial pressure drop. This is making an assumption about what caused the pressure drop, and that the drop is continuous, not temporary.
