To what height can a body weighing 4 tons be raised, spending the same amount

To what height can a body weighing 4 tons be raised, spending the same amount of energy as when heating 3 liters of water from 20 ° C to boiling?

mt = 4 t = 4000 kg.

g = 10 N / kg.

V = 3 l = 3 * 10-3 m3.

t1 = 20 ° C.

t2 = 100 ° C.

C = 4200 J / kg * ° С.

ρ = 1000 kg / m3.

h -?

According to the condition of the problem, the thermal energy Q, which is necessary for heating the water, is converted into the potential energy of the body Ep: Ep = Q.

We express the potential energy of the body En by the formula: En = mt * g * h.

Q = C * m * (t2 –t1).

We express the mass of heated water m by the formula: m = V * ρ.

Q = C * V * ρ * (t2 –t1).

C * V * ρ * (t2 –t1) = mt * g * h.

h = C * V * ρ * (t2 –t1) / mt * g.

h = 4200 J / kg * ° С * 3 * 10-3 m3 * 1000 kg / m3 * (100 ° С – 20 ° С) / 4000 kg * 10 N / kg = 2520 m.

Answer: due to thermal energy, the body can rise to a height of h = 2520 m.