Suppose that the microwave radiation has a wavelength of 12 cmcm . How many photons are required to heat 245 mLmL of coffee from 25.0 ∘C∘C to 62.0 ∘C∘C? Assume that the coffee has the same density, 0.997 g/mLg/mL , and specific heat capacity, 4.184 J/(g⋅K)J/(g⋅K) , as water over this temperature range.

2.281*10^28 photons

Explanation:

Data

Mass of the coffee

   m = D*V = 0.997 * 245 = 244.265 g

Energy (heat) absorbed by the coffee

   Q = m*cp*ΔT = 244.265 * 4.184 * 37 = 37814.1761 J  

Energy of the photon

   E = h*c/λ

where h is the Planck constant ( 6.63 x 10^(-34) J*s) and c is the speed of light at vacuum (3*10^8 m/s)

   E = 6.63 x 10^(-34)*3*10^8/0.12 = 1.6575*10^(-24) J  

number of photons required = total energy required / energy per photon

   n = 37814.1761/1.6575*10^(-24) = 2.281*10^28 photons

in 1783 cavendish was working with his hydrogen gas and found that when he burned it and condensed the vapor it was water. this was very significant since it disproved the greek theory of elements completely since water was not a simple substance but the product of two gases. it was lavoisier who hearing of the experiment gave cavendish's gas the name hydrogen ("water-producer") and added that hydrogen burned by combining with oxygen and that water was a hydrogen-oxygen combination.

explanation: