To what height was a bucket of water with a volume of 10 liters raised if its potential energy is equivalent to the amount

To what height was a bucket of water with a volume of 10 liters raised if its potential energy is equivalent to the amount of heat released during the complete combustion of 0.5 kg of peat?

V = 10 l = 0.01 m3.

ρ = 1000 kg / m3.

g = 10 m / s2.

mt = 0.5 kg.

λ = 15 * 10 ^ 6 J / kg.

Q = En.

h -?

The amount of thermal energy Q, which is released during the complete combustion of peat, can be expressed by the formula: Q = λ * mt, where λ is the specific heat of combustion of peat, mt is the mass of burnt peat.

We will express the potential energy of a bucket with water by the formula: En = m * g * h, where m is the mass of water in the bucket, g is the acceleration of gravity, h is the height of the bucket with water.

We express the mass of water in a bucket by the formula: m = V * ρ.

En = V * ρ * g * h.

λ * mt = V * ρ * g * h.

h = λ * mt / V * ρ * g.

h = 15 * 10 ^ 6 J / kg * 0.5 kg / 0.01 m3 * 1000 kg / m3 * 10 m / s2 = 75000 m.

Answer: if the mass of the bucket itself is neglected, then it can be raised to a height of h = 75000 m.

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