Suppose that the microwave radiation has a wavelength of 10.8 cm. How many photons are required to heat 225 mL of coffee from 25.0*C to 62.0*C ? Assume that the coffee has the same density, 0.997 g/mL , and specific heat capacity, 4.184 J/(gK), as water over this temperature range
Calculate q required to heat the water for the coffee.
q = mass x specific heat x (Tfinal-Tinitial). q = ?? joules.
How many joules do we get out of 1 photon at this wavelength.
E = hc/wavelength = 6.626 x 10^-34 x 3 x 10^8/wavelength in meters.
Then set up a proportion:
(1 photon/energy 1 photon) = (# photons/energy needed)
Solve for # photons. Check the proportion after it is set up to make sure it is right.
thank you :D
To find the number of photons required to heat the coffee, we need to calculate the energy required to raise the temperature.
Step 1: Calculate the mass of the coffee.
Given that the density of the coffee is 0.997 g/mL, and the volume of the coffee is 225 mL, we can calculate the mass using the formula:
mass = density * volume
mass = 0.997 g/mL * 225 mL
mass = 224.325 g (rounded to three decimal places)
Step 2: Calculate the change in temperature.
The change in temperature is given by:
ΔT = final temperature - initial temperature
ΔT = 62.0°C - 25.0°C
ΔT = 37.0°C
Step 3: Calculate the energy required to heat the coffee.
The energy required to heat a substance is given by the formula:
energy = mass * specific heat capacity * change in temperature
energy = 224.325 g * 4.184 J/(gK) * 37.0°C
energy = 34,820.633 J (rounded to three decimal places)
Step 4: Calculate the energy per photon.
The energy of a photon is given by the formula:
energy per photon = Planck's constant * speed of light / wavelength
Planck's constant, h = 6.626 x 10^-34 J*s
Speed of light, c = 3.00 x 10^8 m/s (convert cm to meters)
wavelength = 10.8 cm = 10.8 x 10^-2 m
energy per photon = (6.626 x 10^-34 J*s * 3.00 x 10^8 m/s) / (10.8 x 10^-2 m)
energy per photon = 1.833 x 10^-19 J (rounded to three decimal places)
Step 5: Calculate the number of photons.
The number of photons can be calculated by dividing the total energy required by the energy per photon:
number of photons = energy required / energy per photon
number of photons = 34,820.633 J / 1.833 x 10^-19 J
number of photons = 1.897 x 10^23 photons (rounded to three significant figures)
Therefore, approximately 1.897 x 10^23 photons are required to heat 225 mL of coffee from 25.0°C to 62.0°C.