Enormous numbers of microwave photons are needed to warm macroscopic samples of matter. A portion of soup containing 225 g water is heated in a microwave oven from 23°C to 91°C, with radiation of wavelength 1.55 10-2 m. How many photons are absorbed by the water in the soup?
E = mass water x specific heat water x (Tfinal-Tinitial).
E = 225 x 4.184 x (91-23) = ?? Joules needed.
E = hc/wavelength = ??joules from one photon.
So how many photons are required?
8.6*10^-19
To determine the number of photons absorbed by the water in the soup, we can use the equation:
N = (E / h) * (1 / λ)
where:
N represents the number of photons
E is the energy absorbed by the soup
h is the Planck's constant (approximately 6.63 × 10⁻³⁴ J·s)
λ is the wavelength of radiation
First, let's calculate the energy absorbed by the soup. We can use the equation:
E = m * c * ΔT
where:
E represents the energy absorbed
m is the mass of the soup (225 g or 0.225 kg)
c is the specific heat capacity of water (approximately 4.18 J/g°C or 4,180 J/kg°C)
ΔT is the change in temperature (91°C - 23°C = 68°C)
E = 0.225 kg * 4,180 J/kg°C * 68°C
E ≈ 626,532 J
Now, using the energy absorbed and the given wavelength, we can plug these values into the formula:
N = (626,532 J / (6.63 × 10⁻³⁴ J·s)) * (1 / 1.55 × 10⁻² m)
N ≈ 6.02 × 10³⁴ photons
Therefore, approximately 6.02 × 10³⁴ photons are absorbed by the water in the soup.