Calculating time it takes to heat water in a microwave and the steam to evaporate

Question

I am stuck on a question in my thermodynamics class. We have studied topics such as heat $Q$, entropy $S$, enthalpie $H$, etc.

1. Bob puts a glass containing 500 grams of water in the microwave. Before putting it in, it is at room temperature. However, he falls asleep, and the water heats to $100^\circ C$, evaporating and the microwave then explodes at a pressure of 10 atmospheres. The oven has a power of $1200 W$. How how long does each process take? Make reasonable assumptions for the properties of steam. You can assume that after evaporation the water vapor has a pressure of 1 atmosphere and a temperature of $373^\circ K$.
2. After the explosion, the gas will drop in temperature due to heat transfer. Will the explosion itself counteract or amplify this decline? And what influence does the assumption that steam is or is not an ideal gas have? on this?

Here are my attempts (for simplicity I don't fill in the numbers that are given):

1)

First we break the question up into different processes, and then determine the time that each took.

Phases: A) Water heats up to $100^\circ$ $\rightarrow$ B) Phase transition Water to Steam $\rightarrow$ until $P$ hits 10 atm (microwave explodes)

Determining the time of each:

A) $\Delta T = 100^\circ K$. I can determine the heat which is $Q = m.c.\Delta T$. I know that Power is $P = \frac{W}{\Delta t}$, so thought that maybe I can figure out the time from this. I want to use $Q = U + W$ to figure out what $W$ is equal to, but I don't know how to figure out $U$ in this equation.

B) The water still at $100^\circ$ and during this the $P$ raises until its at 10 atm. I'm assuming that the microwave starts at 1 atm. I also make the assumption that the steam acts like an ideal gas. Therefore, I know that the increase in pressure will be related to the increase in the volume.

I was then thinking of using the ideal gas law $PV = nRT$ to calculate how much of the water has to evaporate ($V$) to increase the pressure enough to 10 atm. The problem is, that since the microwave is a confined space, I don't think it is possible to increase the volume.

Therefore I don't have an expression for how much of the water needs to evaporate, and also not the time needed to do this.

2.

I don't know what the explosion will do, nor do I understand what the influence is of an ideal gas.

Answer 1

First we break the question up into different processes, and then determine the time that each took.
Phases: A) Water heats up to 100∘ → B) Phase transition Water to Steam → until P hits 10 atm (microwave explodes).

Your 2nd step is to broad. It contains a number of smaller steps.

1. Water in glass $V_{glass}$(full to top) from $T_{initial}$ to 100° at 1 atm
2. Water in $V_{glass}$ at 100° to steam in $V_{glass}$ at 100° at 1 atm
3. Steam at 100° in $V_{glass}$ to steam at 100° in $V_{microwave}$ at 1 atm
4. Steam at 100° in $V_{microwave}$ at 1 atm to steam at $T_{final}$ at 10 atm.