A certain microwave oven delivers 633 watts (J/s) of power to a coffee cup containing 53.1 g of water at 25°C. If the wavelength of microwaves in the oven is 9.75 cm, how long does it take, and how many photons must be absorbed, to make the water boil? The specific heat capacity of water is 4.18 J/°C·g. Assume only the water absorbs the energy of the microwave.

___________ s
____________ photons

How many J needed to raise T from 25C to 100 C? That is mass H2O x specific heat H2O x delta T = about 16,000 J but you need to get a more accurate number.

How much energy is available for a photon?
That is E = hc/wavelength =
6.626E-34*3E8/0.0975m = about 2E-24 J/photon.

2E-24 J/photon x # photons = 16,000
Solve for # photons.

633 J/s x # seconds = 16,000
Solve for # seconds.
Check my work. It's getting late.

To solve this problem, we need to find the amount of energy required to heat the water from 25°C to boiling, and then calculate the time it takes and the number of photons absorbed.

First, we need to calculate the energy required to raise the temperature of the water:

1. Calculate the mass of water in grams: 53.1 g
2. Calculate the temperature change: boiling point of water = 100°C, initial temperature = 25°C
ΔT = 100°C - 25°C = 75°C
3. Calculate the energy required using the formula:
energy = mass * specific heat capacity * temperature change
energy = 53.1 g * 4.18 J/°C·g * 75°C

Now, let's calculate the energy required:
energy = 53.1 g * 4.18 J/°C·g * 75°C

Next, we need to determine the number of photons required to deliver this energy. We can use the formula:

energy = number of photons * energy per photon

Since we know the oven power (633 watts) and the wavelength of the microwaves (9.75 cm), we can calculate the energy per photon using the equation:

energy per photon = Planck's constant * speed of light / wavelength

Substitute the values into the equation:
energy per photon = (6.626 x 10^-34 J·s) * (3 x 10^8 m/s) / (9.75 x 10^-2 m)

Now, let's calculate the energy per photon:
energy per photon = (6.626 x 10^-34 J·s) * (3 x 10^8 m/s) / (9.75 x 10^-2 m)

Finally, we can calculate the number of photons using the formula mentioned earlier:

number of photons = energy / energy per photon

Now, let's calculate the number of photons:
number of photons = energy / energy per photon

To find the time it takes, we need to use the power equation:

power = energy / time

Rearranging the equation gives us:

time = energy / power

Now, we can calculate the time:
time = energy / power

Substitute the calculated values for energy and power to find the time.