Suppose that the microwave radiation has a wavelength of 12 cm . How many photons are required to heat 295 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/(g⋅K) , as water over this temperature range. the answer WAS NOT 1.72e47
heat (energy) needed ... 295 * (62.0 - 25.0) * 0.997 * 4.184 Joules
energy per photon = h * c / 12 = 6.63E-34 * 3.00E10 / 12 Joules
divide the heat needed by the energy per photon
heat needed = q = mass x specific heat x (Tfinal-Tinitial)
q = 295 mL x 0.997 g/mL x 4.184 x (62-25) = approx 46,000 J but you need a better answer and not this estimate.
How much energy in joules can you get from 12 cm light.
That is E in joules/photon = hc/wavelength = 6.626E-34 x 3E8/0.12 = 1.66E-24 J.
Then 1.66E-24 J/photon x #photons = approx 46,000 J
Solve for # photons.
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To determine the number of photons required to heat the coffee, we need to follow these steps:
Step 1: Calculate the mass of the coffee.
Given:
Density of coffee = 0.997 g/mL
Volume of coffee = 295 mL
Mass of coffee = Density × Volume
Mass = 0.997 g/mL × 295 mL = 293.815 g
Step 2: Calculate the amount of heat required.
Given:
Specific heat capacity of water (and coffee) = 4.184 J/(g⋅K)
Change in temperature = 62.0 °C - 25.0 °C = 37.0 °C
Q = mcΔT
Q = 293.815 g × 4.184 J/(g⋅K) × 37.0 °C
Q = 447225.754 J
Step 3: Calculate the energy per photon.
The energy of one photon can be calculated using the equation:
E = hc/λ
Where:
E = energy of one photon
h = Planck's constant = 6.626 x 10^-34 J⋅s
c = speed of light = 3 x 10^8 m/s
λ = wavelength = 12 cm = 0.12 m
E = (6.626 x 10^-34 J⋅s) × (3 x 10^8 m/s) / (0.12 m)
E ≈ 1.6555 x 10^-20 J
Step 4: Calculate the number of photons.
Number of photons = Total energy / Energy per photon
Number of photons = 447225.754 J / 1.6555 x 10^-20 J
Number of photons ≈ 2.70 x 10^22 photons
Therefore, the approximate number of photons required to heat the coffee is 2.70 x 10^22 photons.
To calculate the number of photons required to heat the coffee, we first need to determine the energy required to raise the temperature.
Step 1: Calculate the mass of the coffee.
The volume of the coffee is given as 295 mL. Since the density of the coffee is 0.997 g/mL, we can calculate the mass of the coffee:
Mass = Volume x Density
Mass = 295 mL x 0.997 g/mL
Step 2: Calculate the energy required to heat the coffee.
To calculate the energy required to heat the coffee, we use the equation:
Energy = Mass x Specific Heat Capacity x Change in Temperature
The specific heat capacity is given as 4.184 J/(g⋅K).
Change in Temperature = Final Temperature - Initial Temperature
Change in Temperature = 62.0 °C - 25.0 °C
Now, we can calculate the energy required:
Energy = Mass x Specific Heat Capacity x Change in Temperature
Step 3: Calculate the energy of one photon.
The energy of a photon is given by the equation:
Energy = Planck's constant x Speed of light / Wavelength
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.
To convert the wavelength from centimeters to meters, we divide by 100:
Wavelength = 12 cm / 100 = 0.12 m
Now, we can calculate the energy of one photon:
Energy_photon = Planck's constant x Speed of light / Wavelength
Step 4: Calculate the number of photons.
To find the number of photons required to heat the coffee, we divide the total energy required by the energy of one photon:
Number of photons = Energy required / Energy of one photon
Now, you can plug in the values and perform the calculations to find the number of photons required.