Answer:
The mass of water boiled away as steam is 3.24 kg
Step-by-step explanation:
Given;
total food calories consumed, 2000
1 calorie = 4,200 J
total energy of food consumed in joules, Q = 2,000 x 4,200 J = 8,400,000 J
initial temperature of the water, t₁ = 20 ⁰C
Assumptions:
(1) No energy is lost
(2) all the water is boiled to steam
(3) Energy needed to raise water to 100 ⁰C (q₁) plus Energy needed to boil the water to steam (q₂) = total energy of food consumed (Q)
(4) latent heat of vaporization of water, L = 2,260 kJ/kg
(5) specific heat capacity of water, c = 4,200 J/kg⁰C
let the mass of the water = m
Q = q₁ + q₂
Q = mcΔt + mL
Q = mc(t₂ - t₁) + mL
8,400,000 = 4,200(100 - 20)m + 2,260,000m
8,400,000 = 336,000m + 2,260,000m
8,400,000 = 2,596,000 m
m = 8,400,000/2,596,000
m = 3.24 kg
Therefore, the mass of water boiled away as steam is 3.24 kg