Question

Какое количество энергии потребуется для нагревания и плавления свинца массой 0,4 кг, имеющего на чальную тем- пературу 17 °С?

Answer 1

Q=сmΔt (нагревание)
Q=лямбда·m
сначала тело нужно нагреть, только затем начать плавить, т.е. общая формула будет выглядеть так: Qплавления+Qнагревания=Qобщая
⇒ Qобщ = cmΔt+лямбда·m
c(свинца) = 140 дж/(кг·ºС)
лямбда(свинца) = 2,5·10^4
t плавления свинца = 327ºC  ⇒ Δt= 327-17=310ºС
Q = 140·0,4·310+0,4·20000=17360+8000=25360(Дж)

Answer 2

Calculating Energy Required to Heat and Melt Lead

To calculate the energy required to heat and melt lead, we can use the specific heat capacity of lead and the heat of fusion of lead.

Given: - Mass of lead, m = 0.4 kg - Initial temperature, T1 = 17 °C - Melting point of lead, Tm = 327.5 °C - Specific heat capacity of lead, c = 128 J/(kg·°C) - Heat of fusion of lead, L = 2.04 × 10^4 J/kg

Energy Required to Heat Lead to Its Melting Point

The energy required to heat the lead from its initial temperature to its melting point can be calculated using the formula: \[ Q_1 = mc\Delta T \] Where: - Q1 = Energy required to heat the lead - m = Mass of the lead - c = Specific heat capacity of lead - ΔT = Change in temperature

Substitute the given values: \[ Q_1 = 0.4 kg \times 128 J/(kg·°C) \times (327.5 °C - 17 °C) \]

Calculating \( Q_1 \): \[ Q_1 = 0.4 \times 128 \times (327.5 - 17) \] \[ Q_1 = 0.4 \times 128 \times 310.5 \] \[ Q_1 = 15984 J \]

The energy required to heat the lead to its melting point is 15984 J.

Energy Required to Melt the Lead

The energy required to melt the lead can be calculated using the formula: \[ Q_2 = mL \] Where: - Q2 = Energy required to melt the lead - m = Mass of the lead - L = Heat of fusion of lead

Substitute the given values: \[ Q_2 = 0.4 kg \times 2.04 \times 10^4 J/kg \]

Calculating \( Q_2 \): \[ Q_2 = 0.4 \times 2.04 \times 10^4 \] \[ Q_2 = 8160 J \]

The energy required to melt the lead is 8160 J.

Total Energy Required

The total energy required to heat and melt the lead is the sum of \( Q_1 \) and \( Q_2 \): \[ Q_{total} = Q_1 + Q_2 \] \[ Q_{total} = 15984 J + 8160 J \] \[ Q_{total} = 24144 J \]

Therefore, the total energy required to heat and melt 0.4 kg of lead, initially at 17 °C, is 24144 J.