Question

Усложнённая задача по физике: В закрытом сосуде с поршнем, движущемся без трения, находится ненасыщенный водяной пар при температуре 100 ⁰С и относительной влажности 50%. При изотермическом сжатии объем пара уменьшился в 3 раза. Определите давление водяных паров в конечном состоянии. Плотность насыщенных водяных паров при 100 ⁰С равна 0.598 кг/м3, молярная масса 18 г/моль, универсальная газовая постоянная 8.31 Дж/К/моль. Ответ приведите в кПа, округлив до ближайшего целого.

Answer 1

Ответ:

154 кПа

Объяснение:

φ=0.5 (50%)   ρн=0,598 кг/м³    V1=3*V2   M=0.018 кг/моль   T=373 K   p=?

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Первоначальная плотность пара

ρ1=φ*ρн

Плотность после сжатия при T=const

ρ2=ρ1*V1/V2=3*ρ1

p=3*φ*ρн*R*T/M=3*0.5*0.598*8.31*373/0.018≈154*10³ Па

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Answer 2

Problem Analysis

To solve this problem, we need to use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and density, and inversely proportional to its volume. We can use this law to calculate the pressure of the water vapor in the final state after compression.

Given Information

- Initial temperature of the water vapor: 100 °C - Relative humidity: 50% - Initial volume of the vapor: unknown - Final volume of the vapor: 1/3 of the initial volume - Density of saturated water vapor at 100 °C: 0.598 kg/m³ - Molar mass of water: 18 g/mol - Universal gas constant: 8.31 J/(K·mol)

Solution Steps

1. Calculate the initial pressure of the water vapor using the ideal gas law. 2. Calculate the final pressure of the water vapor using the ideal gas law and the given information about the change in volume. 3. Convert the final pressure to kilopascals (kPa) and round to the nearest whole number.

Let's calculate the solution step by step.

Step 1: Calculate the Initial Pressure

To calculate the initial pressure, we need to know the initial volume of the water vapor. Unfortunately, the problem statement does not provide this information. Therefore, we cannot calculate the initial pressure accurately.

Step 2: Calculate the Final Pressure

We know that the final volume of the water vapor is 1/3 of the initial volume. Since the initial volume is unknown, we can assume any value for it. Let's assume an initial volume of 1 m³ for simplicity.

Using the ideal gas law, we can write the equation as follows:

P₁ * V₁ = n * R * T₁

Where: - P₁ is the initial pressure (unknown) - V₁ is the initial volume (1 m³) - n is the number of moles of water vapor - R is the universal gas constant (8.31 J/(K·mol)) - T₁ is the initial temperature (100 °C + 273.15 = 373.15 K)

We can rearrange the equation to solve for the number of moles of water vapor:

n = (P₁ * V₁) / (R * T₁)

Since the volume is reduced to 1/3 of the initial volume, the final volume (V₂) is (1/3) * V₁.

Using the ideal gas law again, we can write the equation for the final state as follows:

P₂ * V₂ = n * R * T₁

Substituting the value of V₂ and rearranging the equation, we can solve for P₂:

P₂ = (n * R * T₁) / V₂

Step 3: Convert the Final Pressure to kPa

To convert the final pressure from pascals (Pa) to kilopascals (kPa), we divide the pressure by 1000.

Now, let's calculate the final pressure.

Calculation

Let's assume an initial volume of 1 m³ for simplicity.

Using the given information: - Initial temperature (T₁) = 100 °C = 373.15 K - Final volume (V₂) = (1/3) * 1 m³ = 1/3 m³ - Density of saturated water vapor at 100 °C = 0.598 kg/m³ - Molar mass of water = 18 g/mol - Universal gas constant (R) = 8.31 J/(K·mol)

First, let's calculate the number of moles of water vapor (n):

n = (P₁ * V₁) / (R * T₁)

Since the initial pressure (P₁) and initial volume (V₁) are unknown, we cannot calculate the number of moles accurately.

Next, let's calculate the final pressure (P₂):

P₂ = (n * R * T₁) / V₂

Since we cannot calculate the number of moles accurately, we cannot calculate the final pressure accurately.

Therefore, we cannot provide a specific answer to this problem without knowing the initial volume of the water vapor.

Please provide the missing information, and we will be happy to help you further.