Question

В сосуде находится жидкость A, объём которой равен 0,5 л. Если добавить в сосуд 0,5 л жидкости B, то средняя плотность содержимого сосуда увеличится на 60 кг/м3. На сколько еще увеличится средняя плотность смеси, если в сосуд добавить еще 0,5 л жидкости B? Считайте, что объём смеси указанных жидкостей равен сумме объёмов компонентов. Ответ выразите в кг/м3, округлите до целого числа. Жидкости не выливаются из сосуда​

Answer 1

Ответ:

плотность увеличится на 20 кг/м³

Объяснение:

пусть плотность жидкостей А и В х и у соответственно. Объем смеси 0,5+0,5=1 л

масса 0,5х+0,5у.

Средняя плотность 0,5(х+у)/1=0,5(x+y)

разница плотностей (x+y)/2-x=(y-x)/2

новый объем 1+0,5=1,5 л

новая масса 0,5х+1у, плотность (0,5х+y)/1,5

разница плотности

(0,5х+y)/1,5-0,5(x+y)=(x+2y)/3-(x+y)/2=(2x+4y-3x-3y)/6=(y-x)/6

(y-x)/2 разница плотностей после первого долития

(y-x)/6 разница после второго долития

увеличение плотности меньше в 3 раза.

60:3=20 кг/м³

Answer 2

Problem Analysis

We have a vessel containing liquid A with a volume of 0.5 liters. When we add 0.5 liters of liquid B to the vessel, the average density of the contents of the vessel increases by 60 kg/m^3. We need to determine how much the average density of the mixture will increase if we add an additional 0.5 liters of liquid B to the vessel.

Solution

To solve this problem, we need to calculate the initial average density of the mixture and then calculate the final average density after adding the additional 0.5 liters of liquid B.

Let's start by calculating the initial average density of the mixture.

Initial Average Density Calculation

The initial volume of the mixture is the sum of the volumes of liquid A and liquid B, which is 0.5 liters + 0.5 liters = 1 liter.

Now, we need to calculate the initial average density. We can use the formula:

Average Density = Total Mass / Total Volume

Since we are given the increase in average density when 0.5 liters of liquid B is added, we can calculate the initial total mass using the formula:

Total Mass = Average Density * Total Volume

Let's calculate the initial total mass:

Total Mass = Average Density * Total Volume = 60 kg/m^3 * 1 liter = 60 kg

Therefore, the initial total mass of the mixture is 60 kg.

Now, we can calculate the initial mass of liquid A. Since the volume of liquid A is 0.5 liters and the density is not given, we cannot directly calculate the mass. Therefore, we need to make an assumption about the density of liquid A.

Let's assume the density of liquid A is x kg/m^3.

Using the formula for mass:

Mass = Density * Volume

The mass of liquid A is:

Mass of A = Density of A * Volume of A = x kg/m^3 * 0.5 liters

Similarly, the mass of liquid B is:

Mass of B = Density of B * Volume of B = y kg/m^3 * 0.5 liters

Since the average density of the mixture is given by:

Average Density = (Mass of A + Mass of B) / Total Volume

We can substitute the values and solve for x:

60 kg/m^3 = (x kg/m^3 * 0.5 liters + y kg/m^3 * 0.5 liters) / 1 liter

Simplifying the equation:

60 kg/m^3 = (0.5x + 0.5y) kg/m^3

Now, we have one equation with two variables (x and y). We need another equation to solve for x and y.

Final Average Density Calculation

To calculate the final average density after adding an additional 0.5 liters of liquid B, we need to consider the new total volume and the new total mass.

The new total volume is 1 liter + 0.5 liters = 1.5 liters.

The new total mass is the sum of the initial total mass and the mass of the additional 0.5 liters of liquid B.

Let's calculate the new total mass:

New Total Mass = Initial Total Mass + Mass of Additional B

The mass of the additional 0.5 liters of liquid B is:

Mass of Additional B = Density of B * Volume of Additional B = y kg/m^3 * 0.5 liters

Therefore, the new total mass is:

New Total Mass = 60 kg + (y kg/m^3 * 0.5 liters)

Now, we can calculate the final average density using the formula:

Final Average Density = New Total Mass / New Total Volume

Substituting the values:

Final Average Density = (60 kg + (y kg/m^3 * 0.5 liters)) / 1.5 liters

Simplifying the equation:

Final Average Density = (40 kg + 0.5y kg/m^3) / 1.5 kg

Therefore, the final average density of the mixture, after adding an additional 0.5 liters of liquid B, is given by:

Final Average Density = (40 + 0.5y) kg/m^3

To find the increase in average density, we subtract the initial average density from the final average density:

Increase in Average Density = Final Average Density - Initial Average Density

Substituting the values:

Increase in Average Density = (40 + 0.5y) kg/m^3 - 60 kg/m^3

Simplifying the equation:

Increase in Average Density = 0.5y - 20 kg/m^3

Therefore, the increase in average density of the mixture, after adding an additional 0.5 liters of liquid B, is given by:

Increase in Average Density = 0.5y - 20 kg/m^3

Now, we need to solve for y to find the increase in average density.

Solving for y

To solve for y, we can use the equation we derived earlier:

60 kg/m^3 = (0.5x + 0.5y) kg/m^3

Simplifying the equation:

60 kg/m^3 = 0.5x kg/m^3 + 0.5y kg/m^3

Since we assumed the density of liquid A as x kg/m^3, we can substitute the value:

60 kg/m^3 = 0.5 * x kg/m^3 + 0.5y kg/m^3

Simplifying the equation:

60 kg/m^3 = 0.5x kg/m^3 + 0.5y kg/m^3

Since the volume of liquid A is 0.5 liters and the density of liquid A is x kg/m^3, we can calculate the mass of liquid A:

Mass of A = Density of A * Volume of A = x kg/m^3 * 0.5 liters

Similarly, the mass of liquid B is:

Mass of B = Density of B * Volume of B = y kg/m^3 * 0.5 liters

Since the average density of the mixture is given by:

Average Density = (Mass of A + Mass of B) / Total Volume

We can substitute the values and solve for y:

60 kg/m^3 = (x kg/m^3 * 0.5 liters + y kg/m^3 * 0.5 liters) / 1 liter

Simplifying the equation:

60 kg/m^3 = (0.5x + 0.5y) kg/m^3

Now, we have one equation with two variables (x and y). We need another equation to solve for x and y.

Unfortunately, the given information does not provide enough information to solve for x and y. We need additional information, such as the densities of liquid A and liquid B, to calculate the increase in average density.

Therefore, without additional information, we cannot determine how much the average density of the mixture will increase if we add an additional 0.5 liters of liquid B to the vessel.

Please let me know if there is anything else I can help you with.