Hey jiskha.
Microwave ovens emit microwave radiation that is absorbed by water. The absorbed radiation is converted to heat that is transferred to other components of the food. Suppose that the microwave radiation has a wavelength of 12.7 cm. How many photons are required to heat 200. mL of coffee from 21°C to 63°C?
I have no clue where to start.
E = hc/wavelength = xx J energy of 1 photon.
How much energy do you need?
q to heat coffee. = mass water x specific heat water x delta T = ?? joules total needed.
so how many of those photons will you need?
?? J/photon x # photons = ??total joules needed.
So you
To solve this question, you will need to use the formula relating energy, wavelength, and the speed of light. Here are the steps you can follow:
Step 1: Convert the given wavelength from centimeters to meters.
- Divide the given wavelength (12.7 cm) by 100 to convert it to meters.
Step 2: Calculate the energy per photon using the formula:
- Energy per photon (E) = Planck's constant (h) × speed of light (c) / wavelength (λ)
- The value of Planck's constant (h) is approximately 6.626 x 10^-34 J·s.
- The speed of light (c) is approximately 3.00 x 10^8 m/s.
Step 3: Calculate the total energy required to heat the coffee using the formula:
- Total energy (E_total) = mass of coffee (m) × specific heat capacity of water (C) × change in temperature (ΔT)
- The mass of coffee is given as 200. mL, which can be converted to grams.
- The specific heat capacity of water is approximately 4.18 J/g·°C.
- The change in temperature (ΔT) is the final temperature (63°C) minus the initial temperature (21°C).
Step 4: Divide the total energy required by the energy per photon to find the number of photons.
- Number of photons (N) = Total energy (E_total) / Energy per photon (E)
Now, let's calculate each step in detail:
Step 1: Convert the given wavelength from centimeters to meters.
- Given wavelength = 12.7 cm = 12.7 / 100 m = 0.127 m
Step 2: Calculate the energy per photon.
- Energy per photon (E) = (6.626 x 10^-34 J·s) × (3.00 x 10^8 m/s) / (0.127 m)
- Energy per photon ≈ 1.563 x 10^-19 J
Step 3: Calculate the total energy required to heat the coffee.
- Mass of coffee = 200. mL = 200. g (since 1 mL of water ≈ 1 g)
- Specific heat capacity of water (C) = 4.18 J/g·°C
- Change in temperature (ΔT) = (63°C) - (21°C) = 42°C
- Total energy (E_total) = (200. g) × (4.18 J/g·°C) × (42°C)
- Total energy ≈ 353,088 J
Step 4: Calculate the number of photons.
- Number of photons (N) = (353,088 J) / (1.563 x 10^-19 J)
- Number of photons ≈ 2.26 x 10^21 photons
Therefore, approximately 2.26 x 10^21 photons are required to heat 200. mL of coffee from 21°C to 63°C.