I am wondering if my work makes sense for the following problem:
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?
My work:
q=heat absorbed by water = mass x specific heat water x delta T
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?
No. Did you read my last post?
number photons= energyneede/energyperphoton
Goodness.
I did read your last post...you asked what q was equal to. And in this post I answered your question what q is equal to.
You are not with me.
Doesn't the question ask how many photons are needed?
You know the total energy needed, q.
You know the energy per photon.
number*energyperphoton=energyneeded.
5.9 x 10^23 ?
To determine if your work is correct, let's go through the steps together.
1. First, you correctly calculated the heat absorbed by the water using the equation q = mass x specific heat water x delta T. The mass of the water is given as 1000 grams (1 L of water has a mass of 1000 g), the specific heat of water is 4.184 J/g°C, and the change in temperature is 10°C. So, q = 1000 g x 4.184 J/g°C x 10°C = 41840 J.
2. Next, you calculated the change in energy (delta E) per photon using the equation deltaE = hc/wavelength. You correctly used the values for Planck's constant (h = 6.626 x 10^-34 Js) and the speed of light (c = 3.0 x 10^8 m/s). The wavelength you used is 2.8 x 10^-6 m. Thus, deltaE = (6.626 x 10^-34 Js x 3.0 x 10^8 m/s) / (2.8 x 10^-6 m) = 7.09 x 10^-20 J/photon.
3. Then, you set up a proportion to find the number of photons needed to heat the water. You correctly set up the proportion as 1 photon = 7.09 x 10^-20 J and q (heat absorbed by the water) = 41840 J. By solving this proportion, you found that the number of photons is 5.894 x 10^-16.
Based on the steps you've provided, your calculations appear to be correct. The number of photons you calculated (5.894 x 10^-16) represents the number of photons needed to heat the given 1.00 L sample of water from 20°C to 30°C by absorbing the infra-red radiation with a wavelength near 2.80 μm.