Suppose that the microwave radiation has a wavelength of 10.8cm . How many photons are required to heat 295ml of coffee from 25.0 C to 62.0 C? Assume that the coffee has the same density, 0.997g/ml , and specific heat capacity, 4.184J/(gk) , as water over this temperature range
First, use the density to convert 295 mL to mass H2O. Then calculate the heat required, call it q, to heat that amount of water from 25 to 62.
q = mass H2O x specific heat H2O x (Tfinal-Tinitial).
Now calculate the amount of energy given off by one photon at this wavelength.
E = hc/wavelength. Wavelength must be in meters. h is Planck's constant. c is speed of light in m/s.
The # photons = q(from above)/E(from above)
73
To calculate the number of photons required to heat the coffee, we need to follow these steps:
Step 1: Calculate the mass of coffee.
The volume of the coffee is given as 295 ml, and the density of the coffee is given as 0.997 g/ml. Therefore, we can calculate the mass of the coffee using the formula:
Mass = Volume x Density
Mass = 295 ml x 0.997 g/ml
Step 2: Calculate the energy required to heat the coffee.
The specific heat capacity of the coffee is given as 4.184 J/(g·K). To calculate the energy required to heat the coffee, we will use the formula:
Energy = Mass x Specific Heat Capacity x Change in Temperature
The change in temperature is given as 62.0°C - 25.0°C.
Step 3: Calculate the energy per photon.
The energy per photon can be calculated using the formula:
Energy per photon = (Planck's constant x Speed of light) / Wavelength
Planck's constant is approximately 6.626 x 10^-34 J·s, and the speed of light is approximately 3.0 x 10^8 m/s. The wavelength should be converted from cm to meters.
Step 4: Divide the total energy required by the energy per photon.
The number of photons can be calculated by dividing the total energy required to heat the coffee by the energy per photon.
Let's calculate the number of photons now:
Step 1: Calculating the mass of coffee.
Mass = 295 ml x 0.997 g/ml
Step 2: Calculating the energy required to heat the coffee.
Energy = Mass x Specific Heat Capacity x Change in Temperature
Step 3: Calculating the energy per photon.
Energy per photon = (Planck's constant x Speed of light) / Wavelength
Step 4: Calculating the number of photons.
Number of photons = Total energy required / Energy per photon
Now, go ahead and substitute the values into these formulas to calculate the number of photons required to heat the coffee.