Answer:
Number of moles of photons required = 5.04 × 10⁴ moles
Explanation:
The energy of a photon can be calculated from Planck's equation E = hc/λ
Where h = 6.63 × 10-³⁴ Js and c, the velocity of light = 3.0 × 10⁸ m/s
Energy of one mole of photons = N₀ × hc/λ
wavelength of photon, λ = 520 nm = 5.20 × 10-⁷ m
Energy of one mole of photons = 6.02 × 10²³ × 6.63 × 10−³⁴ × 3 × 10⁸/5.20 × 10-⁷
Energy of one mole of photons = 2.30 × 10⁵ J/mol
Energy required to raise the temperature of a given mass of a substance, E = mcΔT
Where m is mass of substance, c is specific heat capacity, ΔT is temperature difference
Mass ofnwternin the pool = volume × density
Volume of water = Volume of swimming pool
Volume of water = 16 × 34 × 6 ft³ = 3264 ft³
1 ft³ = 28316.8 cm³; 3264 ft³ = 28316.8 × 3264 = 92426035.2 cm³
Density of water = 1 g/cm³
Mass of water = 92426035.2 cm³ × 1 g/cm³ = 92426035.2g
ΔT = 80°C - 50°C = 30°C, c = 4.18 J/g/K
Energy required to raise 92426035.2 g water by 30° C = 92426035.2 × 4.18 × 30
Energy required = 1.16 × 10¹⁰ J
Hence, number of moles of photons required = 1.16 × 10¹⁰ J/2.30 × 10⁵ J/mol
Number of moles of photons required = 5.04 × 10⁴ moles
