Question

В теплоизолированном сосуде содержится смесь m1 = 1 кг воды и m2 = 100 г льда при температуре tₒ = 0 °С. В сосуд вводят m3 = 5 г пара при температуре t3 = 100 °С. Какой будет температура θ °С в сосуде после установления теплового равновесия? Теплоемкость сосуда не учитывать. Ответ представьте в кельвинах .

Answer 1

Решение в прикреплении

Answer 2

Calculation of Final Temperature in Insulated Vessel

To calculate the final temperature in the insulated vessel after thermal equilibrium is reached, we need to consider the heat transfer between the substances in the vessel. The heat gained or lost by each substance can be calculated using the formula:

Q = m * c * ΔT

Where: - Q is the heat gained or lost - m is the mass of the substance - c is the specific heat capacity of the substance - ΔT is the change in temperature

In this case, we have three substances in the vessel: water, ice, and steam. Let's calculate the heat gained or lost by each substance and then determine the final temperature.

1. Heat gained or lost by water: - Mass of water (m1) = 1 kg - Initial temperature of water (t1) = 0 °C - Final temperature of water (θ) = ? - Specific heat capacity of water (c1) = 4.18 kJ/kg°C (approximately)

Using the formula Q = m * c * ΔT, we can calculate the heat gained or lost by water as follows:

Q1 = m1 * c1 * (θ - t1)

2. Heat gained or lost by ice: - Mass of ice (m2) = 100 g = 0.1 kg - Initial temperature of ice (t2) = 0 °C - Final temperature of ice (θ) = ? - Specific heat capacity of ice (c2) = 2.09 kJ/kg°C (approximately)

Using the formula Q = m * c * ΔT, we can calculate the heat gained or lost by ice as follows:

Q2 = m2 * c2 * (θ - t2)

3. Heat gained or lost by steam: - Mass of steam (m3) = 5 g = 0.005 kg - Initial temperature of steam (t3) = 100 °C - Final temperature of steam (θ) = ? - Specific heat capacity of steam (c3) = 2.03 kJ/kg°C (approximately)

Using the formula Q = m * c * ΔT, we can calculate the heat gained or lost by steam as follows:

Q3 = m3 * c3 * (θ - t3)

To determine the final temperature (θ), we need to ensure that the total heat gained by the substances is equal to the total heat lost. In other words, the sum of the heat gained or lost by each substance should be zero:

Q1 + Q2 + Q3 = 0

Now, let's solve the equation to find the final temperature (θ) in Kelvin.

Calculation Steps:

1. Convert the masses of water, ice, and steam to kilograms: - m1 = 1 kg - m2 = 0.1 kg - m3 = 0.005 kg

2. Substitute the values into the heat transfer equations: - Q1 = m1 * c1 * (θ - t1) - Q2 = m2 * c2 * (θ - t2) - Q3 = m3 * c3 * (θ - t3)

3. Sum up the heat transfer equations and set it equal to zero: - Q1 + Q2 + Q3 = 0

4. Solve the equation for θ.

Please note that the specific heat capacities used in this calculation are approximate values. The actual specific heat capacities may vary slightly depending on the conditions.

Let's perform the calculations to find the final temperature (θ) in Kelvin.