Question

Suppose an oven's radiation wavelength is 0.125 m. a container with 350.00 g of water was placed in the oven, and the temperature of the water rose from 20.0°c to 80.0°c. how many photons of this microwave radiation were required to heat the water? (assume that all the energy from the radiation was used to raise the temperature of the water.) the specific heat of water is 4.18 j/g°c.

Answer 1

The heat (energy) needed to raise the temperature of the water is given by
$Q=m C_S (T_f - T_i)=(350.0 g)(4.18 J/gC)(80C-20C)=87780 J$

The wavelength of the radiation of the oven is $\lambda=0.125 m$, so the energy of a single photon of this radiation is
$E=h \frac{c}{\lambda}=(6.6 \cdot 10^{-34}J) \frac{3\cdot 10^8 m/s}{0.125 m}=1.6 \cdot 10^{-24} J$

So, the number of photons required to heat the water is the total energy absorbed by the water divided by the energy of a single photon:
$N= \frac{Q}{E}= \frac{87780 J}{1.6\cdot 10^{-24}J}= 5.5 \cdot 10^{28}$ photons