How many degrees will a piece of lead weighing 2 kg heat up when it falls to the ground

| September 17, 2021 | education

How many degrees will a piece of lead weighing 2 kg heat up when it falls to the ground from a height of 21.3 m, if all the mechanical energy of the lead turns into its internal energy?

m = 2 kg.

h = 21.3 m.

g = 10 m / s2.

C = 140 J / kg * ° C.

E = Q.

Δt -?

At the beginning of the fall, the total mechanical energy of the body consists only of the potential energy E = En. Let us express the value of potential energy by the formula: En = m * g * h, where m is the mass of the body, g is the acceleration of gravity.

The amount of heat energy that goes into heating the lead ball is expressed by the formula: Q = C * m * Δt, where C is the specific heat of lead, m is the mass of the ball, Δt is the change in its temperature.

Since by the condition of the problem E = Q, then m * g * h = C * m * Δt.

Δt = m * g * h / C * m = g * h / C.

Δt = 10 m / s2 * 21.3 m / 140 J / kg * ° C = 1.5 ° C.

Answer: The temperature of the ball will increase by Δt = 1.5 ° C.



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