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college Chemistry

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Warm objects emit electromagnetic radiation in the infra-red region. Heat lamps employ this principle to generate infra-red radiation. Water absorbs infra-red 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 infra-red radiation, and its temperature increases from 20C to 30C. How many photons of this radiation are used to heat the water?

  • college Chemistry - ,

    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 - ,

    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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