Question

Шар объёмом о,1 м3 ,сделанный из тонкой бумаги,наполняют горячим воздухом,имеющим температуру 340 К. Температура окружающего воздуха 290 К. Давление воздуха внутри шара и атмосферное одинаковы и равны 100 кПа. При какой массе бумажной оболочки шар будет подниматься?

Answer 1

Ответ на задачу будет 18грамм

Answer 2

Calculation of the mass of the paper envelope

To calculate the mass of the paper envelope required for the balloon to ascend, we need to consider the buoyant force acting on the balloon. The buoyant force is equal to the weight of the air displaced by the balloon.

The buoyant force can be calculated using the formula:

Buoyant force = Weight of the air displaced = Density of air x Volume of air displaced x g

Where: - Density of air is the density of air at the given temperature and pressure. - Volume of air displaced is the volume of the balloon. - g is the acceleration due to gravity.

To find the mass of the paper envelope, we can rearrange the formula as follows:

Mass of the paper envelope = (Buoyant force) / g

Let's calculate the mass of the paper envelope step by step.

Step 1: Calculate the density of air

The density of air can be calculated using the ideal gas law:

Density of air = (Pressure of air) / (Gas constant x Temperature of air)

Where: - Pressure of air is the atmospheric pressure. - Gas constant is a constant value. - Temperature of air is the temperature of the surrounding air.

Given that the atmospheric pressure and the pressure inside the balloon are both 100 kPa, and the temperature of the surrounding air is 290 K, we can calculate the density of air.

Step 2: Calculate the volume of air displaced

The volume of air displaced by the balloon is equal to the volume of the balloon itself. Given that the balloon has a volume of 0.1 m^3, we can use this value for the volume of air displaced.

Step 3: Calculate the buoyant force

Now that we have the density of air and the volume of air displaced, we can calculate the buoyant force using the formula mentioned earlier.

Step 4: Calculate the mass of the paper envelope

Finally, we can calculate the mass of the paper envelope by dividing the buoyant force by the acceleration due to gravity.

Let's perform the calculations.

Calculation:

Step 1: Calculate the density of air: - Pressure of air = 100 kPa - Gas constant = a constant value - Temperature of air = 290 K

Step 2: Calculate the volume of air displaced: - Volume of air displaced = 0.1 m^3

Step 3: Calculate the buoyant force: - Buoyant force = (Density of air) x (Volume of air displaced) x g

Step 4: Calculate the mass of the paper envelope: - Mass of the paper envelope = (Buoyant force) / g

Please note that the exact values for the gas constant and acceleration due to gravity are not provided in the question. To obtain a precise answer, these values need to be known.