From the original assumptions:
So far, my understanding of water evaporating is the following:
The higher the temperature, the higher the vapor pressure, therefore the faster water vaporizes.
The rate of water boiling, assuming a constant boiling temperature, is dependent on the rate of heat transfer to the water, not the vapor pressure.
At sea level, water boils at 100°c. Boiling temperature decreases as athmospheric pressure decreases.
It is somewhat more correct to say that the boiling temperature decreases as ambient pressure decreases, no matter what the source of the ambient pressure.
It takes a fixed amount of heat / energy to evaporate water (once it reaches boiling point?)
The heat of vaporization of water decreases as the boiling temperature (and boiling pressure) increases, up to the critical temperature (and critical pressure) of water. This means that if pressure changes substantially during the boiling process, the heat of vaporization of the water will also change substantially during the boiling process.
To answer the question directly, there are a few industrial situations where water is given enough heat to instantly evaporate if. For the case of hot oil systems in industry, a furnace heats up the oil to 450 deg F (maybe hotter), and sends the oil to process equipment for the purpose of boiling the process in a heat exchanger. Very infrequently (approximately 5 year cycles), the hot oil system is shut down for maintenance, and water is used to hydroblast equipment in order to clean it. This means that water collects in low points in the associated piping. After maintenance is complete, the proper start-up procedure calls for slowly heating the oil, checking all low points in the piping for water, and draining all water before the hot oil gets above the boiling point of water. On very rare occasions, there have been cases where a small slug of water was trapped in piping during startup without anyone knowing it. This slug of water was isolated from the hot oil by closed valves, so its temperature was too low to cause boiling. Unfortunately, in the event of a process operator opening those valves (for whatever reason), the trapped slug of water immediately contacts 450 deg F hot oil, causing an extremely rapid evaporation rate, and resulting in an explosion. And yes, this has indeed happened. So the answer is: if the water has access to enough heat, at a high enough temperature, it will indeed instantly vaporize.
Best Answer
First think how much energy causes a temperature change from -12.15 to 0 degrees Celsius.
$Q = mc\delta T = 150 \times 2.1 \times 12.15 = 3827.25 kJ$
We now have 55,034.175 - 3827 = 51207Kj remaining.
Now Ice is converted into water. The energy required to convert Ice into Water is given by:
$Q = mL_f$, where $L_f$ is the latent heat of fusion for water, which is 334.
Therefore,
$Q = 150\times 334 = 50100kJ$
We therefore now have 51207-50100 = 1107kJ remaining.
So to determine how much this raises the temperature from 0, we use the formula,
$Q = mc\delta T$
Therefore,
$1107 = 150\times 4.2 \times \delta T$
Therefore
$\delta T = 1.76$
Therefore final temperature is 1.76 degrees Celsius.