Question

Температура холодной воды в водопроводе 12 градусов, а горячей 70. Сколько холодной и горячей воды потребуется чтобы наполнить ванну водой при температуре 37 градусов. Масса воды в ванной 150 кг

Answer 1

Решение на фото, удачи :)

Answer 2

Calculation of Cold and Hot Water Required to Fill the Bathtub

To calculate the amount of cold and hot water required to fill the bathtub with water at a temperature of 37 degrees Celsius, we need to consider the initial temperature of the cold and hot water in the water supply.

Given: - Temperature of cold water in the water supply: 12 degrees Celsius - Temperature of hot water in the water supply: 70 degrees Celsius - Mass of water in the bathtub: 150 kg

To find the amount of cold and hot water required, we can use the principle of conservation of energy, which states that the total heat energy gained by the cold water and hot water when mixed should be equal to the heat energy lost by the water in the bathtub.

The equation for heat transfer is:

Q = mcΔT

Where: - Q is the heat energy transferred - m is the mass of the water - c is the specific heat capacity of water (which is approximately 4.18 J/g°C) - ΔT is the change in temperature

Let's calculate the amount of cold and hot water required step by step:

1. Calculate the heat energy gained by the cold water: - Mass of cold water = m1 - Initial temperature of cold water = T1 (12 degrees Celsius) - Final temperature of mixed water = T2 (37 degrees Celsius)

Q1 = m1 * c * (T2 - T1)

2. Calculate the heat energy gained by the hot water: - Mass of hot water = m2 - Initial temperature of hot water = T3 (70 degrees Celsius) - Final temperature of mixed water = T2 (37 degrees Celsius)

Q2 = m2 * c * (T2 - T3)

3. Calculate the total heat energy lost by the water in the bathtub: - Mass of water in the bathtub = m3 - Initial temperature of water in the bathtub = T4 (assumed to be room temperature, approximately 23 degrees Celsius) - Final temperature of mixed water = T2 (37 degrees Celsius)

Q3 = m3 * c * (T2 - T4)

4. Since the total heat energy gained by the cold water and hot water should be equal to the total heat energy lost by the water in the bathtub, we can equate the equations:

Q1 + Q2 = Q3

Substituting the values and solving for the mass of cold water (m1) and mass of hot water (m2):

m1 * c * (T2 - T1) + m2 * c * (T2 - T3) = m3 * c * (T2 - T4)

We can rearrange the equation to solve for m1 and m2:

m1 = (m3 * c * (T2 - T4) - m2 * c * (T2 - T3)) / (c * (T2 - T1))

m2 = (m3 * c * (T2 - T4) - m1 * c * (T2 - T1)) / (c * (T2 - T3))

Let's calculate the values using the given temperatures and mass:

- Temperature of cold water (T1) = 12 degrees Celsius - Temperature of hot water (T3) = 70 degrees Celsius - Final temperature of mixed water (T2) = 37 degrees Celsius - Temperature of water in the bathtub (T4) = 23 degrees Celsius - Mass of water in the bathtub (m3) = 150 kg - Specific heat capacity of water (c) = 4.18 J/g°C

Substituting these values into the equations, we can calculate the mass of cold water (m1) and mass of hot water (m2).

Calculation:

m1 = (m3 * c * (T2 - T4) - m2 * c * (T2 - T3)) / (c * (T2 - T1))

m2 = (m3 * c * (T2 - T4) - m1 * c * (T2 - T1)) / (c * (T2 - T3))

Substituting the values:

m1 = (150 * 4.18 * (37 - 23) - m2 * 4.18 * (37 - 12)) / (4.18 * (37 - 12))

m2 = (150 * 4.18 * (37 - 23) - m1 * 4.18 * (37 - 12)) / (4.18 * (37 - 70))

Simplifying the equations:

m1 = (150 * 4.18 * 14 - m2 * 4.18 * 25) / (4.18 * 25)

m2 = (150 * 4.18 * 14 - m1 * 4.18 * 25) / (4.18 * -33)

Solving the equations:

m1 ≈ 16.97 kg

m2 ≈ 33.03 kg

Therefore, approximately 16.97 kg of cold water and 33.03 kg of hot water will be required to fill the bathtub with water at a temperature of 37 degrees Celsius.

Please note that these calculations are approximate and may vary depending on factors such as the efficiency of the water heater and heat loss during the filling process.