Respuesta :
Explanation:
It is known that relation between heat energy and temperature change is as follows.
Q = [tex]mC \Delta T[/tex]
where, q = heat energy
m = mass of the solution or solvent
[tex]\Delta T[/tex] = change in temperature
Hence, putting the given values into the above formula as follows.
Q = [tex]mC \Delta T[/tex]
= [tex]110.0 g \times \frac{315 J}{75^{o}C} \times (100 - 25)^{o}C[/tex]
= 34650 J
Now, calculate the energy of photons at wavelength 3.02 mm as follows.
E = [tex]\frac{hc}{\lambda}[/tex]
where, h = planks constant = [tex]6.626 \times 10^{-34} Js[/tex]
c = velocity of light = [tex]3 \times 10^{8}[/tex] m/s
[tex]\lambda[/tex] = wavelength = 3.02 mm = [tex]3.02 \times 10^{-3}[/tex] m (as 1 m = 1000 mm)
Therefore, putting the given values into the above formula as follows.
E = [tex]\frac{hc}{\lambda}[/tex]
= [tex]\frac{6.626 \times 10^{-34} Js \times 3 \times 10^{8} m/s}{3.02 \times 10^{-3} m}[/tex]
= [tex]6.58 \times 10^{-23}[/tex] J
Now, the number of photons required of energy [tex]6.58 \times 10^{-23}[/tex] J/photon for the total energy of 34650 J as follows.
[tex]E_{total} = n \times E[/tex]
n = [tex]\frac{E_{total}}{E}[/tex]
= [tex]\frac{34650 J}{6.58 \times 10^{-23}}[/tex]
= [tex]5265.95 \times 10^{23}[/tex] photons
or, = [tex]5.265 \times 10^{26}[/tex] photons
Thus, we can conclude that the minimum number of photons present are [tex]5.265 \times 10^{26}[/tex].
