Question

В теплоизолированный сосуд помещают воду массой 50 граммов при положительной температуре 20 градусов Цельсия и лёд массой 1 килограмм при отрицательной температуре -20 градусов Цельсия. Определить конечное состояние системы (конечную температуру и мамы вещества в жидком и твёрдом состоянии).

Answer 1

Initial State of the System

In the given scenario, we have a thermally insulated vessel containing water with a mass of 50 grams and a positive temperature of 20 degrees Celsius. Additionally, there is ice with a mass of 1 kilogram and a negative temperature of -20 degrees Celsius.

Determining the Final State of the System

To determine the final state of the system, we need to consider the principle of energy conservation and the heat transfer that occurs between the water and the ice.

When the water and ice come into contact, heat will flow from the water to the ice until they reach thermal equilibrium. This means that the heat lost by the water will be equal to the heat gained by the ice.

To calculate the final temperature, we can use the equation:

m1 * c1 * (Tf - T1) = m2 * c2 * (T2 - Tf)

Where: - m1 is the mass of water (50 grams) - c1 is the specific heat capacity of water (4.18 J/g°C) - Tf is the final temperature (unknown) - T1 is the initial temperature of the water (20°C) - m2 is the mass of ice (1 kilogram) - c2 is the specific heat capacity of ice (2.09 J/g°C) - T2 is the initial temperature of the ice (-20°C)

By substituting the given values into the equation, we can solve for the final temperature (Tf).

50g * 4.18 J/g°C * (Tf - 20°C) = 1000g * 2.09 J/g°C * (-20°C - Tf)

Simplifying the equation:

209(Tf - 20) = -2000(Tf + 20)

Solving for Tf:

209Tf - 4180 = -2000Tf - 40000

209Tf + 2000Tf = 40000 - 4180

2209Tf = 35820

Tf = 35820 / 2209 ≈ 16.2°C

Therefore, the final temperature of the system will be approximately 16.2 degrees Celsius.

Mass of Water and Ice in their Respective States

To determine the mass of water and ice in their respective states (liquid and solid), we need to consider the conservation of mass.

The total mass of the system remains constant throughout the process. Therefore, the mass of water and ice in their final states will be the same as their initial masses.

Hence, the mass of water in its liquid state will be 50 grams, and the mass of ice in its solid state will be 1 kilogram.

Summary

In summary, when a thermally insulated vessel contains water with a mass of 50 grams at a positive temperature of 20 degrees Celsius and ice with a mass of 1 kilogram at a negative temperature of -20 degrees Celsius, the final state of the system will be as follows: - The final temperature of the system will be approximately 16.2 degrees Celsius. - The mass of water in its liquid state will be 50 grams. - The mass of ice in its solid state will be 1 kilogram.

Please note that the calculations provided are based on the given information and assumptions about the specific heat capacities of water and ice.