A container with 0.485 L of water is placed into microwave and is then radiated

Question

A container with 0.485 L of water is placed into microwave and is then radiated with electromagnetic energy that has a wavelength of 12.1 cm. The temperature of the water then rose by 89.7 ?C. Calculate the number of photons that were absorbed by the water. Assume water has a density of 1.00 g?mL?1 and its specific heat is 4.184 J?g?1??C?1

A container with 0.485 L of water is placed into microwave and is then radiated with electromagnetic energy that has a wavelength of 12.1 cm. The temperature of the water then rose by 89.7 degree C. Calculate the number of photons that were absorbed by the water. Assume water has a density of 1.00 g.mL-1 and its specific heat is 4.184 J. g-1 degree C-1

Explanation / Answer

V = 0.485 L = 0.485 kg

m = 485 g of water

WL = 12.1 cm

dT = 89.7°C

find photons absorbed

First, identify the heat absorbed:

Q = m*C*(Tf-Ti)

Q = 485*4.184*(89.7)

Q = 182022.828 J

Now;

WL = h c / E

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

E = energy per particle J/photon

E = (6.626*10^-34)(3*10^8)/(0.121) = 1.6428*10^-24 J/photons

then

n photons = Q/E =182022.828 /( 1.6428*10^-24)

n photons = 1.10800*10^29 photons released

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