Question

Assume that water absorbs light of wavelength 4.20*10^-6 m with 100% efficiency. How many photons are required to heat 5.75 g of water by 1.00 K at this wavelength? The heat capacity of water is 75.5 J mol^-1 K^-1

Answer 1

Let´s find how much energy is needed to heat water:

Q= mol x Cp x DT

In this case Dt is 1K, mass is 5.75g and Cp is the heat capacity of water wich is 75.5 J/molK.

mol of water= 5.75g/18g/mol= 0.31944

Q= 0.31944mol x 75.5 J/molK x 1K = 24.1181 J

Now, the energy contained in 1 photon is:

E= hc/lambda

h= palnck´s constant (6.67x10^-34 J.s)

c= speed of light (3x10⁸ m/s)

lambda= wavelength

E= (6.67x10^-34 J.s x 3x10⁸ m/s) / 4.20x10^-6 m = 4.76x10^-20 J

This is the energy that 1 photon can give to the water, now, how many photons we need to achieve the energy we need, wich is 24.0695 J?

1 photon ------------ 4.76x10^-20 J

x= 5.07x10²⁰ photons --------- 24.1181 J