Respuesta :
Answer:
[tex]n = 1.96 \times 10^{28}[/tex] photons
Explanation:
Mass of the coffee is given as
[tex]mass = density\times volume[/tex]
here we know that
density = 0.997 g/ml
volume = 225 ml
now mass of coffee will be
[tex]m = 0.997 \times 225 = 224.325 g[/tex]
now heat required to raise the temperature of coffee will be
[tex]Q = ms\Delta T[/tex]
[tex]Q = 224.325 \times 4.184 \times (62 - 25)[/tex]
[tex]Q = 34727.3 J[/tex]
now we know that energy of one photon is
[tex]E = \frac{hc}{\lambda}[/tex]
[tex]E = \frac{(6.6 \times 10^{-34}) ( 3 \times 10^8)}{0.112}[/tex]
[tex]E = 1.77 \times 10^{-24} J[/tex]
now it requires "n" photons to complete the energy
[tex]n\times (1.77 \times 10^{-24}) = 34727.3[/tex]
[tex]n = 1.96 \times 10^{28}[/tex]
The number of photons that are required to heat 225 ml of coffee from 25.0 °C to 62 °c
n = 1.962 × 10^(28) photons
We are given;
Wavelength; λ = 11.2 cm = 0.112 m
density; ρ = 0.997 g/ml
volume; V = 225 ml
Specific heat capacity; c = 4.184 J/g.k
Change in temperature;
Δt = (273 + 62) - (273 + 25) K = 37 K
Formula for mass given density and volume is;
m = Vρ
Thus; mass of coffee;
m = 225 × 0.997
m = 224.325 g
Now, formula for Quantity of heat required to raise the temperature is;
Q = mcΔt
Thus;
Q = 224.325 × 4.184 × 37
Q = 34,727.3046 J
Now, we know that formula for energy of photon is; E = hc/λ
Where;
h is Planck's constant = 6.6 × 10^(-34) J.s
c is speed of light = 3 × 10^(8) m/s
λ is wavelength.
Thus;
E = [6.6 × 10^(-34) × 3 × 10^(8)]/0.112
E = 1.77 × 10^(-24) J
To get the number of photons required, we will use the formula;
n = Q/E
Thus;
n = 34,727.3046/(1.77 × 10^(-24))
n = 1.962 × 10^(28) photons
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