Question

Для получения воды с температурой 40 градусов к 5 кг кипятка при 100 градусов добавили холодную воду, имеющей температуру 10 градусов. Сколько холодной воды было добавлено? С решением, пожалуйста

Answer 1

Теплоемкость воды: с = 4,187 * 10³ Дж/ кг*К
Происходит два процесса охлаждение 5 кг кипятка (Q охл) Δt охл = 100 - 40 = 60 и нагревание неизвестной массы воды от 10 градусов (Q нагр) Δt нагр = 40 - 10 = 30. Количество теплоты в обоих случаях по модулю одинаковое, отличается только знаком.
Q охл = cm*Δt охл =  4,187 * 10³ * 5 * 60 = 1,256 * 10^6 Дж
Q нагр = Q охл
Q охл = cm*Δt нагр, отсюда m = Q охл / (с*Δt) = 1,256 * 10^6 / (4,187 * 10³ * 30) = 10 кг.

Answer 2

Calculating the Amount of Cold Water Added to Hot Water

To calculate the amount of cold water added to hot water to achieve a final temperature of 40 degrees Celsius, we can use the principle of mixtures. The formula for this calculation is:

m1c1(Tf - T1) = -m2c2(Tf - T2)

Where: - m1 = mass of the hot water - c1 = specific heat capacity of water - Tf = final temperature - T1 = initial temperature of the hot water - m2 = mass of the cold water - c2 = specific heat capacity of water - T2 = initial temperature of the cold water

Let's calculate the amount of cold water added using the given values: - Initial temperature of hot water (T1) = 100 degrees Celsius - Mass of hot water (m1) = 5 kg - Initial temperature of cold water (T2) = 10 degrees Celsius - Final temperature (Tf) = 40 degrees Celsius

Using the formula, we can solve for the mass of cold water (m2).

Calculation

Using the formula m1c1(Tf - T1) = -m2c2(Tf - T2), we can calculate the mass of cold water added.

Given: - m1 = 5 kg - c1 = specific heat capacity of water (approximately 4.18 J/g°C) - Tf = 40°C - T1 = 100°C - c2 = specific heat capacity of water (approximately 4.18 J/g°C) - T2 = 10°C

Plugging in the values: 5 * 4.18 * (40 - 100) = -m2 * 4.18 * (40 - 10)

Solving for m2: -208.5 = -30.54m2 m2 ≈ 6.83 kg

Answer

Approximately 6.83 kg of cold water was added to the hot water to achieve a final temperature of 40 degrees Celsius.