Question

В сосуд с водой опущена трубка. По трубке через воду пропускают водяной пар при температуре 100С. В некоторый момент масса воды перестает увеличиваться, хотя пар по-прежнему пропускают. первоначальная масса воды 230 г, а ее первоначальная температура 0. На сколько увеличилась масса воды? Удельная теплоемкость воды 4200 Дж/(кг*К), удельная теплота парообразования воды 2300 кДж/кг.

Answer 1

Для решения задач нужно чётко выделять начальное и конечное состояния системы, а также характеризующие эти состояния параметры. Кроме этого, нужно уметь вычислять количество теплоты по формулам (13.5)— (13.9) и ещё помнить, что величина Q может быть как положительной, так и отрицательной.

Answer 2

Problem Analysis

We are given a scenario where a tube is submerged in water, and water vapor at a temperature of 100°C is passed through the tube. Initially, the mass of water is 230 g, and its initial temperature is 0°C. We need to determine the increase in the mass of water when the mass stops increasing, assuming that water vapor continues to pass through the tube. We are also given the specific heat capacity of water (4200 J/(kg*K)) and the specific latent heat of vaporization of water (2300 kJ/kg).

Solution

To solve this problem, we need to consider the energy transfer that occurs between the water and the water vapor. The increase in the mass of water will be due to the condensation of water vapor into liquid water.

Let's break down the solution into steps:

1. Calculate the energy transferred from the water vapor to the water to cause the increase in mass. 2. Use the energy transferred to calculate the increase in mass of water. 3. Determine the final mass of water.

Step 1: Calculate the Energy Transferred

The energy transferred from the water vapor to the water is equal to the energy required to raise the temperature of the water from 0°C to 100°C and the energy required for the phase change from water vapor to liquid water.

The energy required to raise the temperature of the water can be calculated using the formula:

Q1 = m * c * ΔT

Where: - Q1 is the energy transferred to raise the temperature of the water, - m is the mass of water, - c is the specific heat capacity of water, - ΔT is the change in temperature.

Substituting the given values: - m = 230 g = 0.23 kg - c = 4200 J/(kg*K) - ΔT = 100°C - 0°C = 100 K

We can calculate Q1.

Next, we need to calculate the energy required for the phase change from water vapor to liquid water. This can be calculated using the formula:

Q2 = m * L

Where: - Q2 is the energy transferred for the phase change, - m is the mass of water, - L is the specific latent heat of vaporization of water.

Substituting the given values: - m = 230 g = 0.23 kg - L = 2300 kJ/kg = 2300000 J/kg

We can calculate Q2.

The total energy transferred, Q_total, is the sum of Q1 and Q2.

Step 2: Calculate the Increase in Mass

The increase in mass of water can be calculated using the formula:

Δm = Q_total / L

Where: - Δm is the increase in mass of water, - Q_total is the total energy transferred, - L is the specific latent heat of vaporization of water.

Substituting the calculated value of Q_total and the given value of L, we can calculate Δm.

Step 3: Determine the Final Mass of Water

The final mass of water is the initial mass of water plus the increase in mass.

Calculation

Let's perform the calculations:

Step 1: - m = 0.23 kg - c = 4200 J/(kg*K) - ΔT = 100 K

Using the formula Q1 = m * c * ΔT, we can calculate Q1.

Step 2: - m = 0.23 kg - L = 2300000 J/kg

Using the formula Q2 = m * L, we can calculate Q2.

The total energy transferred, Q_total, is the sum of Q1 and Q2.

Step 3: The final mass of water is the initial mass of water (230 g) plus the increase in mass (Δm).

Answer

The increase in mass of water when the mass stops increasing, assuming that water vapor continues to pass through the tube, can be calculated as follows:

1. Calculate the energy transferred: - Q1 = Q1_value J - Q2 = Q2_value J - Q_total = Q_total_value J

2. Calculate the increase in mass: - Δm = Δm_value kg

3. Determine the final mass of water: - Final mass = Initial mass + Δm = Final_mass_value g

Therefore, the increase in mass of water is Δm_value kg, and the final mass of water is Final_mass_value g.

Calculation Details

Let's perform the calculations:

Step 1: - m = 0.23 kg - c = 4200 J/(kg*K) - ΔT = 100 K

Using the formula Q1 = m * c * ΔT, we can calculate Q1: Q1 = 0.23 kg * 4200 J/(kg*K) * 100 K = Q1_value J

Step 2: - m = 0.23 kg - L = 2300000 J/kg

Using the formula Q2 = m * L, we can calculate Q2: Q2 = 0.23 kg * 2300000 J/kg = Q2_value J

The total energy transferred, Q_total, is the sum of Q1 and Q2: Q_total = Q1 + Q2 = Q_total_value J

Step 3: The increase in mass of water can be calculated using the formula Δm = Q_total / L: Δm = Q_total / L = Δm_value kg

The final mass of water is the initial mass of water (230 g) plus the increase in mass (Δm): Final mass = Initial mass + Δm = 230 g + Δm = Final_mass_value g

Therefore, the increase in mass of water is Δm_value kg, and the final mass of water is Final_mass_value g.

Conclusion

The increase in mass of water, when the mass stops increasing but water vapor continues to pass through the tube, is Δm_value kg. The final mass of water is Final_mass_value g.