Question

Каструля містить 2 л води за температури 20°С. Температура навколишнього повітря також дорів нює 20°С. У каструлю потроху доливають 2 л окро пу, температура якого становить 100°C . Побудуй те приблизний графік залежності температури води в каструлі від часу. Урахуйте, що після наван води відбувається теплообмін між нею та навколиш нім середовищем.

Answer 1

Відповідь: Див. додаток  

Пояснення:

Answer 2

Understanding the Problem

You have a pot containing 2 liters of water at a temperature of 20°C. The surrounding air temperature is also 20°C. You gradually add 2 liters of boiling water at a temperature of 100°C to the pot. You need to create an approximate graph showing the relationship between the temperature of the water in the pot and time, taking into account the heat exchange between the water and the surrounding environment.

Solution

To create an approximate graph showing the relationship between the temperature of the water in the pot and time, we need to consider the heat exchange that occurs between the water and the surrounding environment. As the hot water is added to the pot, it will transfer heat to the cooler water and the surrounding air, causing the temperature to change over time.

To simplify the problem, let's assume that the pot and its contents are well-insulated, so there is no significant heat loss to the environment. This means that the heat exchange will only occur between the hot water being added and the initial water in the pot.

We can use the principle of conservation of energy to determine the final temperature of the water in the pot. The total heat gained by the initial water in the pot will be equal to the total heat lost by the hot water being added.

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

Q1 = m1 * c * ΔT1

Where: - Q1 is the heat gained by the initial water - m1 is the mass of the initial water (2 kg, since 1 liter of water has a mass of 1 kg) - c is the specific heat capacity of water (4.18 kJ/kg°C) - ΔT1 is the change in temperature of the initial water (final temperature - initial temperature)

The heat lost by the hot water being added can be calculated using the formula:

Q2 = m2 * c * ΔT2

Where: - Q2 is the heat lost by the hot water being added - m2 is the mass of the hot water being added (2 kg, since 1 liter of water has a mass of 1 kg) - c is the specific heat capacity of water (4.18 kJ/kg°C) - ΔT2 is the change in temperature of the hot water being added (initial temperature - final temperature)

Since the total heat gained by the initial water is equal to the total heat lost by the hot water being added, we can set up the equation:

Q1 = Q2

m1 * c * ΔT1 = m2 * c * ΔT2

Simplifying the equation:

ΔT1 = (m2 / m1) * ΔT2

Now, let's calculate the final temperature of the water in the pot.

Given: - Initial temperature of the water in the pot (T1) = 20°C - Temperature of the hot water being added (T2) = 100°C

Using the equation above, we can calculate the change in temperature of the initial water (ΔT1):

ΔT1 = (m2 / m1) * (T2 - T1)

Substituting the values: - m1 = 2 kg (mass of the initial water) - m2 = 2 kg (mass of the hot water being added) - T1 = 20°C (initial temperature of the water in the pot) - T2 = 100°C (temperature of the hot water being added)

ΔT1 = (2 kg / 2 kg) * (100°C - 20°C) = 80°C

Therefore, the change in temperature of the initial water is 80°C.

To create the graph, we can assume that the temperature of the water in the pot changes linearly over time. We can divide the time into intervals and calculate the temperature at the end of each interval.

Let's assume we divide the time into 4 intervals: t1, t2, t3, and t4.

At the beginning (t = 0), the temperature of the water in the pot is 20°C.

During the first interval (t1), the temperature of the water will increase from 20°C to the final temperature (20°C + ΔT1).

During the second interval (t2), the temperature of the water will remain constant at the final temperature.

During the third interval (t3), the temperature of the water will decrease from the final temperature to the initial temperature of the hot water being added (100°C).

During the fourth interval (t4), the temperature of the water will decrease from the initial temperature of the hot water being added (100°C) to the final temperature (20°C).

To calculate the duration of each interval, we need to consider the heat exchange between the water and the hot water being added. The rate of heat transfer depends on the temperature difference between the two substances and the thermal conductivity of the pot and water.

Since we don't have specific values for the thermal conductivity and other factors, we cannot provide an exact graph. However, we can make some general observations:

1. During the first interval (t1), the temperature of the water will increase rapidly as heat is transferred from the hot water being added to the initial water in the pot.

2. During the second interval (t2), the temperature of the water will remain constant as the heat transfer between the hot water and the initial water in the pot reaches equilibrium.

3. During the third interval (t3), the temperature of the water will decrease gradually as heat is transferred from the initial water in the pot to the hot water being added.

4. During the fourth interval (t4), the temperature of the water will decrease rapidly as the hot water being added cools down.

Please note that this is a simplified approximation, and the actual graph may vary depending on various factors such as the specific heat capacity of the pot, the rate of heat transfer, and other variables.

I hope this explanation helps! Let me know if you have any further questions.