Physics Practice Problems #1

OK, so someone asked for help with this problem.

Heating 235g of water from 22.6C to 94.4C in a microwave oven requires 7.06 x 10⁴J of energy. If the microwave frequency is 2.88 x 10⁵s^-1, how many quanta are required to supply the 7.06 x 10⁴J?

You only really need from the question are the frequency of the microwaves (2.88•10⁵s^-1), the temperature change (22.6C to 94.4C), and the total energy (7.06•10⁴J). First, we turn the frequency into a wavelength.

λ=c/f
c=299,792,458 m/s
f=2.88•10⁵s^-1
λ=299,792,458/(2.88•10⁵) m•s/s
λ=1040.49603

Next, we need to find the temperature change.
T₀=22.6°C=295.75K
T₁=94.4°C=367.55K

T=T₁-T₀
T=367.55-295.75
T=71.8

Next, we'll need a few constants.
Planck's Constant: h=6.626068•10^-34 m²kg/s
Boltzmann's Constant: 1.3806503•10^-23 m²•kg•s^-2•K^-1
e=2.71828183

Now, we're ready to find the energy of one photon, but we need a formula.

You use all the values in that formula and you get 9.91306903•10^-22 J per photon.

Now all you need to do is divide the total energy by the amount of energy each photon caries.

(7.06•10⁴J)/(9.91306903•10^-22J)
7.12191147•10²⁵

So it takes 7.12191147•10²⁵ photons to heat the water, but we need to remember to round to the appropriate number of digits. We started wit 3-digit numbers, so we have to end with a 3-digit number. The final answer is 7.12•10²⁵ photons.

Thanks to Wikipedia for the picture of the formula.