Question

У бак, що містить 10 кг води при температурі 20 °С, кинули шматок заліза масою 2 кг, нагрітий до температури 500 °С. При цьому деяка кількість води перетворилася на пару. Кінцева температура, що встановилася у баку дорівнює 4 °С. Визначте масу води, що перетворилася на пару.

Answer 1

Problem Analysis

We have a tank containing 10 kg of water at a temperature of 20 °C. A piece of iron weighing 2 kg and heated to a temperature of 500 °C is thrown into the tank. As a result, some of the water is converted into steam. The final temperature in the tank is 4 °C. We need to determine the mass of water that has been converted into steam.

Solution

To solve this problem, we can use the principle of conservation of energy. The heat gained by the water and the iron is equal to the heat lost by the water that has been converted into steam.

Let's break down the solution into steps:

1. Calculate the heat gained by the water and the iron. 2. Calculate the heat lost by the water that has been converted into steam. 3. Equate the two quantities of heat and solve for the mass of water that has been converted into steam.

Step 1: Calculate the heat gained by the water and the iron

The heat gained by the water can be calculated using the formula:

Q_water = m_water * c_water * (T_final - T_initial)

Where: - Q_water is the heat gained by the water - m_water is the mass of water - c_water is the specific heat capacity of water (4.186 J/g°C) - T_final is the final temperature of the system (4 °C) - T_initial is the initial temperature of the water (20 °C)

Substituting the given values, we can calculate the heat gained by the water.

Step 2: Calculate the heat lost by the water that has been converted into steam

The heat lost by the water that has been converted into steam can be calculated using the formula:

Q_steam = m_steam * L_vaporization

Where: - Q_steam is the heat lost by the water that has been converted into steam - m_steam is the mass of water that has been converted into steam - L_vaporization is the latent heat of vaporization of water (2260 J/g)

We need to find the mass of water that has been converted into steam.

Step 3: Equate the two quantities of heat and solve for the mass of water that has been converted into steam

Since the heat gained by the water and the iron is equal to the heat lost by the water that has been converted into steam, we can equate the two quantities of heat:

Q_water + Q_iron = Q_steam

Substituting the formulas for Q_water and Q_steam, we can solve for m_steam.

Let's calculate the mass of water that has been converted into steam.

Calculation

Step 1: Calculate the heat gained by the water Q_water = m_water * c_water * (T_final - T_initial)

Substituting the given values: Q_water = 10 kg * 4.186 J/g°C * (4 °C - 20 °C)

Calculating the value of Q_water: Q_water = -669.76 kJ

Step 2: Calculate the heat lost by the water that has been converted into steam Q_steam = m_steam * L_vaporization

We need to find the mass of water that has been converted into steam.

Step 3: Equate the two quantities of heat and solve for the mass of water that has been converted into steam Q_water + Q_iron = Q_steam

Substituting the values of Q_water and Q_iron: -669.76 kJ + 2 kg * c_iron * (T_final - T_initial) = m_steam * L_vaporization

Simplifying the equation: -669.76 kJ + 2 kg * c_iron * (4 °C - 500 °C) = m_steam * 2260 J/g

Solving for m_steam: m_steam = (-669.76 kJ + 2 kg * c_iron * (4 °C - 500 °C)) / 2260 J/g

Substituting the value of c_iron (specific heat capacity of iron) as 0.45 J/g°C: m_steam = (-669.76 kJ + 2 kg * 0.45 J/g°C * (4 °C - 500 °C)) / 2260 J/g

Calculating the value of m_steam: m_steam ≈ 0.59 kg

Therefore, the mass of water that has been converted into steam is approximately 0.59 kg.

Please note that the calculations provided are based on the given information and assumptions.