Question

В сосуд налили 1 кг воды при температуре 90 °С. Чему равна масса воды, взятой при 30 °С, которую нужно налить в сосуд, чтобы в нём установилась температура воды, равная 50 °С? Потерями энергии на нагревание сосуда и окружающего воздуха пренебречь

Answer 1

речь идет о тепловом балансе..где Q1 = Q2

Q1 = m *c *(t2-t1)

Q2 = m2 * c *(t1-t3)

Q1 = 1 * 4200 * (90-50)

Q2 = m2 * 4200 * (50-30)

с - удельная теплоемкость воды - 4200

немного поясню:

температура которая должна быть в сосуде 50 градусов, значит вода которая находится в сосуде массой 1кг при температуре 90 градусов  остудить до температуры 50 градусов.каким образом? налив в сосуд воду при температуре 30 градусов..

приравниваем:

1 * 4200 * (90-50) = m2 * 4200 * (50-30)

m2 = 40 / 20 = 2 кг

Answer 2

Calculation of the Mass of Water at 30°C

To calculate the mass of water at 30°C that needs to be added to the vessel in order to reach a temperature of 50°C, we can use the principle of heat transfer. The heat gained by the water at 90°C is equal to the heat lost by the water at 30°C when they reach a common temperature of 50°C.

The heat gained by the water at 90°C can be calculated using the formula:

Q1 = m1 * c * (t2 - t1)

Where: - Q1 is the heat gained by the water at 90°C - m1 is the mass of water at 90°C - c is the specific heat capacity of water (approximately 4.18 J/g°C) - t2 is the final temperature (50°C) - t1 is the initial temperature (90°C)

The heat lost by the water at 30°C can be calculated using the same formula:

Q2 = m2 * c * (t2 - t1)

Where: - Q2 is the heat lost by the water at 30°C - m2 is the mass of water at 30°C

Since the heat gained and lost are equal, we can set up the equation:

Q1 = Q2

m1 * c * (t2 - t1) = m2 * c * (t2 - t1)

Simplifying the equation, we get:

m1 = m2 * (t2 - t1) / (t1 - t2)

Now we can substitute the given values into the equation to find the mass of water at 30°C.

Given: - m1 = 1 kg (mass of water at 90°C) - t1 = 90°C (initial temperature) - t2 = 50°C (final temperature)

Substituting the values into the equation:

m2 = 1 kg * (50°C - 30°C) / (90°C - 50°C)

Calculating the result:

m2 = 1 kg * 20°C / 40°C

m2 = 0.5 kg

Therefore, the mass of water at 30°C that needs to be added to the vessel is 0.5 kg.