I don't even understand how this question works. How do I solve it?

A microwave oven heats by radiating food with microwave radiation, which is absorbed by the food and converted to heat. suppose an oven's microwave is 13.7 cm. a container w/ 175 mL of water was placed in the oven and the temp rose from 23.2 dgerees c to 98.7 degrees c. how many photons of this microwave radiation were required? assume all the energy from the radiation was used to raise the temp of the h20.

i would show some work but i don't even know where to begin. :[

q absorbed by water = mass x heat capacity x delta T. Calculate amount of heat generated by oven. q will be in joules.

Then Energy = hc/lambda.
h is Planck's constant, c is speed of light in meters/sec and you have lambda (I guess 13 cm is lambda but you don't say that). That will give you energy of the microwave for 1 photon. You should be able to take it from there.

thanks a bunch!

To solve this question, we need to calculate the number of photons of microwave radiation required to heat the water. Let's break down the problem step by step.

Step 1: Calculate the energy absorbed by the water:
To calculate the energy absorbed by the water, we need to use the formula: Energy = mass * specific heat capacity * change in temperature.

Given:
Mass of water (m) = 175 mL = 175 grams (since the density of water is 1 g/mL)
Specific heat capacity of water (c) = 4.18 J/g·°C (assuming the water has a density of 1 g/mL)
Change in temperature (ΔT) = Final temperature - Initial temperature = (98.7°C - 23.2°C)

Now, substitute the values into the formula:
Energy (E) = mass * specific heat capacity * change in temperature

Step 2: Calculate the energy of one photon:
The energy (E) of a photon can be calculated using the equation: E = h * f, where h is Planck's constant (6.63 x 10^-34 J·s) and f is the frequency of the microwave radiation.

Step 3: Calculate the number of photons:
The number of photons can be calculated by dividing the total energy absorbed by the energy of one photon:
Number of photons = Energy absorbed / Energy of one photon

Now, let's calculate each step:

Step 1: Energy absorbed by the water:
Energy (E) = mass * specific heat capacity * change in temperature
E = (175 g) * (4.18 J/g·°C) * (98.7°C - 23.2°C)

Step 2: Energy of one photon:
E = h * f

Step 3: Number of photons:
Number of photons = Energy absorbed / Energy of one photon

By performing these calculations, you should be able to find the number of photons of microwave radiation required to heat the water.