Question

24 of 29 Review | Constants 1 Periodic Table Part A Suppose that the microwave radiation has a wavelength of 12 cm. How many photons are required to heat 265 mL of coffee from 25.0°C to 62.0°C? Assume that the coffee has the same density 0.997 g/mL, and specific heat capacity, 4.184 J/(8.K), as water over this temperature range. Express the number of photons numerically. ► View Available Hint(s) IVO ALO * mo ? photons Submit Next >

Answer 1

Given:

Density of water is 1 g/mL and volume here is 265 mL/.

So,

m = 265 g

C = 4.184 J/g.oC

Ti = 25 oC

Tf = 62 oC

use:

Q = m*C*(Tf-Ti)

Q = 265.0*4.184*(62.0-25.0)

Q = 41024 J

This is the heat required

Given:

lambda = 12 cm = 0.12 m

1st calculate energy of 1 photon

use:

E = h*c/lambda

=(6.626*10^-34 J.s)*(3.0*10^8 m/s)/(0.12 m)

= 1.657*10^-24 J

number of photon = total energy/energy of 1 photon

n = 41024.0/1.657*10^-24

= 2.477*10^28

Answer: 2.48*10^28