Posted by Need Help on Sunday, December 6, 2009 at 11:51am.
Warm objects emit electromagnetic radiation in the infrared region. Heat lamps employ this principle to generate infrared radiation. Water absorbs infrared radiation with wavelengths near 2.80um. Suppose this radiation is absorbed by the water and converted to heat. A 1.00 L sample of water absorbs infrared radiation, and its temperature increases from 20C to 30C. How many photons of this radiation are used to heat the water?

college Chemistry  DrBob222, Sunday, December 6, 2009 at 11:58am
q=heat absorbed by water = mass x specific heat water x delta T. Assuming the density of water is 1.00 g/L, the mass of 1.0 L is 1,000 grams.
q = 1000 x 4.184 J/g*K x 10.
delta E = hc/wavelength.
Plug in h, c, and wavelength to calculate delta E. That is the energy per photon. Then set up a proportion to determine the number of photons required to reach q.
Post your work if you get stuck.

college Chemistry  Need Help, Sunday, December 6, 2009 at 12:23pm
Thanks for the speedy response!
Here is my work:
q = 1000 x 4.184 x 10
q = 41840
detalE = hc/wavelenght
wavelenght = 2.8 x 10^6 m
deltaE = [(6.626 x 10^34)(3.0 x 10^8)]/2.8 x 10^6
delta E = 7.09 x 10^20 m per photon
Proportion:
1 photon = 7.099 x 10^20m
q = 41840
Therefore, 5.894 x 10^16
Is this correct? Thanks again for you help!
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