Question

Прямая цилиндрическая медная проволока диаметром d покрыта слоем льда толщиной 0,25d. Температура льда и проволоки составляет 0∘C. Если пустить по проволоке постоянный электрический ток, то лёд растает за 10 минут. За какое время он бы растаял, если толщина слоя льда была равна 0,5d, а величина тока и диаметр проволоки были бы те же самые? Ответ выразить в минутах, округлив до целых. Считать, что лёд и вода не проводят электрический ток. Теплопотерями в окружающую среду пренебречь.

Answer 1

Δt1=10 мин   h1=0.25d    h2=0.5d   Δt2=?

Q1=I²*R*Δt1=λ*m1

Q2=I²*R*Δt2=λ*m2

m1=po*V1=po*L*S1       S1=(π/4)*(d+0.25d)² - π*d²/4=π*0.56*d²/4

m2=po*V2=po*L*S2       S2=π*1.75*d²/4

Q2/Q1=Δt2/Δt1=1.75/0.56=3,125         Δt2=31.25 мин

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Answer 2

To solve this problem, we need to consider the heat transfer between the wire and the ice. The heat transfer can be calculated using the equation:

Q = m * c * ΔT

Where: - Q is the heat transfer - m is the mass of the ice - c is the specific heat capacity of ice - ΔT is the change in temperature

Since the ice is at 0°C and the wire is at a higher temperature, heat will flow from the wire to the ice, causing the ice to melt.

Let's assume the initial mass of the ice is M, and the final mass of the ice after melting is 0. We can then calculate the heat transfer required to melt the ice:

Q = M * c * ΔT

Now, let's consider the situation where the ice layer is 0.25d thick. The mass of the ice can be calculated as the volume of the ice multiplied by its density:

M = V * ρ

The volume of the ice can be calculated as the difference in volume between the wire with ice and the wire without ice:

V = π * (r^2 - (r - 0.25d)^2) * L

Where: - r is the radius of the wire - L is the length of the wire

The density of ice, ρ, is approximately 917 kg/m^3.

Now, let's consider the situation where the ice layer is 0.5d thick. We can use the same equations to calculate the mass of the ice and the heat transfer required.

Finally, we can calculate the ratio of the heat transfers for the two situations:

Ratio = (Q_0.5d) / (Q_0.25d)

To find the time it takes for the ice to melt when the ice layer is 0.5d thick, we can use the ratio of the heat transfers and the given time for the ice layer of 0.25d:

Time_0.5d = Ratio * 10 minutes

Let's calculate the values step by step.