Question

Microwave ovens heat food by creating microwave electromagnetic radiation that is absorbed by water molecules in the food.

Answer 1

Explanation:

It is known that relation between heat energy and temperature change is as follows.

             Q = $mC \Delta T$

where, q = heat energy

            m = mass of the solution or solvent

     $\Delta T$ = change in temperature

Hence, putting the given values into the above formula as follows.

            Q = $mC \Delta T$

                = $110.0 g \times \frac{315 J}{75^{o}C} \times (100 - 25)^{o}C$

                = 34650 J

Now, calculate the energy of photons at wavelength 3.02 mm as follows.

             E = $\frac{hc}{\lambda}$

where,     h = planks constant = $6.626 \times 10^{-34} Js$

                c = velocity of light = $3 \times 10^{8}$ m/s

            $\lambda$ = wavelength = 3.02 mm = $3.02 \times 10^{-3}$ m   (as 1 m = 1000 mm)

Therefore, putting the given values into the above formula as follows.

              E = $\frac{hc}{\lambda}$

                 = $\frac{6.626 \times 10^{-34} Js \times 3 \times 10^{8} m/s}{3.02 \times 10^{-3} m}$

                = $6.58 \times 10^{-23}$ J

Now, the number of photons required of energy $6.58 \times 10^{-23}$ J/photon for the total energy of 34650 J as follows.

                $E_{total} = n \times E$

                     n = $\frac{E_{total}}{E}$

                        = $\frac{34650 J}{6.58 \times 10^{-23}}$

                        = $5265.95 \times 10^{23}$ photons

or,                     = $5.265 \times 10^{26}$ photons

Thus, we can conclude that the minimum number of photons present are $5.265 \times 10^{26}$.