Question

У теплоїзольованій посудині міститься 2 кг льоду. Коли у посудину влили 4 кг теплої води, половина льоду розтанула. Коли влили ще 4 кг лоьду такої води - весь лід розтанув і встановилась температура 4С. Якою була початкова температура льоду.

Answer 1

6 C холода это элементарно ))))))))))))))))))))))))))))))

Answer 2

Problem Analysis

We have a well-insulated vessel containing 2 kg of ice. When 4 kg of warm water is poured into the vessel, half of the ice melts. Then, an additional 4 kg of ice is poured into the vessel, causing all the ice to melt and the temperature to stabilize at 4°C. We need to determine the initial temperature of the ice.

Solution

Let's assume the initial temperature of the ice is T°C.

When 4 kg of warm water is poured into the vessel, half of the ice melts. This means that the heat gained by the ice from the warm water is equal to the heat lost by the warm water. The heat gained by the ice can be calculated using the formula:

Q1 = m1 * Lf

where: - Q1 is the heat gained by the ice, - m1 is the mass of the ice that melted, and - Lf is the latent heat of fusion of ice.

The heat lost by the warm water can be calculated using the formula:

Q2 = m2 * Cp * (T2 - T)

where: - Q2 is the heat lost by the warm water, - m2 is the mass of the warm water, - Cp is the specific heat capacity of water, and - T2 is the initial temperature of the warm water.

Since half of the ice melts, we can write:

m1 = 0.5 * 2 kg = 1 kg

Substituting the values into the equations, we have:

Q1 = 1 kg * Lf

Q2 = 4 kg * Cp * (T2 - T)

Since the heat gained by the ice is equal to the heat lost by the warm water, we can write:

Q1 = Q2

1 kg * Lf = 4 kg * Cp * (T2 - T)

Now, let's consider the second scenario where an additional 4 kg of ice is poured into the vessel. This time, all the ice melts and the temperature stabilizes at 4°C. The heat gained by the ice can be calculated using the formula:

Q3 = m3 * Lf

where: - Q3 is the heat gained by the ice, and - m3 is the mass of the ice that melted.

The heat lost by the warm water can be calculated using the formula:

Q4 = m4 * Cp * (T4 - T2)

where: - Q4 is the heat lost by the warm water, - m4 is the mass of the warm water, and - T4 is the final temperature of the warm water.

Since all the ice melts, we can write:

m3 = 4 kg

Substituting the values into the equations, we have:

Q3 = 4 kg * Lf

Q4 = 4 kg * Cp * (T4 - T2)

Since the heat gained by the ice is equal to the heat lost by the warm water, we can write:

Q3 = Q4

4 kg * Lf = 4 kg * Cp * (T4 - T2)

Now, let's solve the system of equations to find the initial temperature of the ice.

Calculation

From the first equation, we have:

1 kg * Lf = 4 kg * Cp * (T2 - T)

Simplifying, we get:

Lf = 4 Cp * (T2 - T)

From the second equation, we have:

4 kg * Lf = 4 kg * Cp * (T4 - T2)

Simplifying, we get:

Lf = Cp * (T4 - T2)

Since both equations are equal to Lf, we can equate them:

4 Cp * (T2 - T) = Cp * (T4 - T2)

Simplifying, we get:

4 T2 - 4 T = T4 - T2

Rearranging the equation, we get:

**5