Water is exposed to infrared radiation of wavelength 3.0×10^−4 cm. Assume that all the radiation is absorbed and converted to heat.
How many photons will be required to raise the temperature of 1.7 g of water by 2.2 K?
planck's constant*Numberphotons* speedligh/wavelength = mcDeltaTemp
on m, the mass of water, make certian it is in the right units, depending on c.
To determine the number of photons required to raise the temperature of water by a certain amount, we need to calculate the energy of each photon and then use that information to find the total energy required to raise the temperature.
First, let's calculate the energy of a single photon using the equation:
E = hc/λ
Where:
E is the energy of a photon
h is Planck's constant (6.626 x 10^-34 J·s)
c is the speed of light (3.00 x 10^8 m/s)
λ is the wavelength of the radiation in meters
First, we convert the wavelength from cm to meters:
λ = 3.0 x 10^-4 cm = 3.0 x 10^-6 m
Now, we can calculate the energy of a single photon:
E = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s) / (3.0 x 10^-6 m)
E ≈ 6.98 x 10^-20 J
Next, we need to calculate the total energy required to raise the temperature of the water by 2.2 K. We can use the specific heat capacity of water (4.18 J/g·K) to find this value.
Q = mcΔT
Where:
Q is the heat energy required
m is the mass of water
c is the specific heat capacity of water
ΔT is the change in temperature
Since we want to raise the temperature of 1.7 g of water by 2.2 K, we have:
Q = (1.7 g)(4.18 J/g·K)(2.2 K)
Q ≈ 16.944 J
Finally, we can determine the number of photons by dividing the total energy (Q) by the energy of a single photon (E):
Number of photons = Q / E
Number of photons ≈ 16.944 J / (6.98 x 10^-20 J)
Number of photons ≈ 2.43 x 10^21 photons
Therefore, approximately 2.43 x 10^21 photons will be required to raise the temperature of 1.7 g of water by 2.2 K.