The average temperature of the top ice balls in Antarctica is -56C. How much gasoline do you need to burn

The average temperature of the top ice balls in Antarctica is -56C. How much gasoline do you need to burn in an ice melter with an efficiency of 25% to have 200 L of water at 60C?

t1 = – 56 “C.

t2 = 0 “C.

t3 = 60 “C.

V = 200 L = 0.2 m ^ 3.

ρ = 1000 kg / m ^ 3.

Sv = 4200 J / kg * “C.

Sl = 2100 J / kg * “C.

λ = 4.6 * 10 ^ 7 J / kg.

k = 3.4 * 10 ^ 5 J / kg.

Efficiency = 25%.

mb -?

To obtain water from ice, the amount of heat Qw is required, which is determined by the formula: Qw = V * ρ * Cl * (t2 – t1) + k * V * ρ + V * ρ * Sv * (t3 – t2).

When gasoline is burned, the amount of heat is released Qb = λ * mb.

Let us write down the formula for determining the efficiency: efficiency = Qw * 100% / Qb.

Efficiency = (V * ρ * Sl * (t2 – t1) + k * V * ρ + V * ρ * Sv * (t3 – t2)) * 100% / λ * mb.

mb = (V * ρ * Sl * (t2 – t1) + k * V * ρ + V * ρ * Sv * (t3 – t2)) * 100% / λ * efficiency.

mb = (0.2 m ^ 3 * 1000 kg / m ^ 3 * 2100 J / kg * “C * (0” c + 56 “C) + 3.4 * 10 ^ 5 J / kg * 0.2 m ^ 3 * 1000 kg / m ^ 3 + 0.2 m ^ 3 * 1000 kg / m ^ 3 * 4200 J / kg * “C * (60” C – 0 “C)) * 100% / 4.6 * 10 ^ 7 J / kg * 25% = 12.34 kg.

Answer: you need to burn mb = 12.34 kg of gasoline.