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
Energy = hc/wavelength. Make sure you change wavelength to meters. E in joules and that is for one(1) photon.
q for water = mass x specific heat x delta T. Use density to determine mass coffee.
So haw many photons will be required to get that many joules?
To determine the number of photons required to heat the coffee, we need to calculate the amount of energy needed to raise the temperature of the coffee from 25.0°C to 62.0°C, and then divide that by the energy per photon.
Step 1: Calculate the mass of the coffee:
Mass of coffee = Volume of coffee × Density
Mass of coffee = 225 mL × 0.997 g/mL
Step 2: Calculate the change in temperature:
Change in temperature = Final temperature - Initial temperature
Change in temperature = 62.0°C - 25.0°C
Step 3: Calculate the energy needed to raise the temperature:
Energy = Mass × Specific heat capacity × Change in temperature
Energy = Mass of coffee × Specific heat capacity × Change in temperature
Step 4: Convert the energy to joules:
Energy (Joules) = Energy (calories) × 4.184 J/cal
Step 5: Calculate the energy per photon:
Energy per photon = Speed of light / Wavelength
Step 6: Calculate the number of photons:
Number of photons = Energy / Energy per photon
Let's now calculate the values step-by-step:
Step 1: Calculate the mass of the coffee:
Mass of coffee = 225 mL × 0.997 g/mL
Mass of coffee = 224.325 g
Step 2: Calculate the change in temperature:
Change in temperature = 62.0°C - 25.0°C
Change in temperature = 37.0°C
Step 3: Calculate the energy needed to raise the temperature:
Energy = Mass × Specific heat capacity × Change in temperature
Energy = 224.325 g × 4.184 J/(gK) × 37.0 K
Step 4: Convert the energy to joules:
Energy (Joules) = Energy (calories) × 4.184 J/cal
Energy (Joules) = Energy × 4.184 J/cal
Step 5: Calculate the energy per photon:
Energy per photon = Speed of light / Wavelength
Energy per photon = 3.00 × 10^8 m/s / (10.8 cm × 0.01 m/cm)
Step 6: Calculate the number of photons:
Number of photons = Energy / Energy per photon
Please provide me with the value for the energy per photon, so that we can continue the calculation.
To answer this question, we need to calculate the amount of heat needed to raise the temperature of the coffee and then convert it into the number of photons required. Here is the step-by-step explanation to solve this problem:
Step 1: Calculate the mass of the coffee.
Given that the density of the coffee is 0.997 g/mL and the volume is 225 mL, we can calculate the mass using the formula mass = density x volume:
mass = 0.997 g/mL x 225 mL = 224.325 g
Step 2: Calculate the heat required to raise the temperature.
We can use the specific heat capacity of water to calculate the amount of heat needed using the formula Q = mass x specific heat capacity x change in temperature:
Q = 224.325 g x 4.184 J/(gK) x (62.0°C - 25.0°C) = 36,210.57 J
Step 3: Convert the heat energy into photons.
We can use the formula E = hc/λ to calculate the energy of one photon, where E is the energy, h is Planck's constant (6.626 x 10^-34 J.s), c is the speed of light (2.998 x 10^8 m/s), and λis the wavelength (10.8 cm or 0.108 m).
E = (6.626 x 10^-34 J.s)(2.998 x 10^8 m/s)/(0.108 m)
E ≈ 1.848 x 10^-20 J
To find the number of photons, we can divide the amount of heat energy by the energy of one photon:
Number of photons = 36,210.57 J / (1.848 x 10^-20 J) ≈ 1.96 x 10^23 photons
Therefore, approximately 1.96 x 10^23 photons are required to heat 225 mL of coffee from 25.0°C to 62.0°C.