Question

Задача. Кислородный баллон объемом V=75 л заправлен до давления p1=9,9 МПа и хранится на открытом воздухе при температуре -9 градусов. Определите, каково будет давление p2 газа в баллоне, если его перенести в тепловое помещениие с температурой 27 градусов

Answer 1

Problem:

We are given a oxygen cylinder with a volume of V = 75 L, filled to a pressure of p1 = 9.9 MPa, and stored in open air at a temperature of -9 degrees Celsius. We need to determine the pressure p2 of the gas in the cylinder if it is transferred to a heated room with a temperature of 27 degrees Celsius.

Solution:

To solve this problem, we can use the ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are related by the equation:

PV = nRT

Where: - P is the pressure of the gas - V is the volume of the gas - n is the number of moles of gas - R is the ideal gas constant - T is the temperature of the gas in Kelvin

We can rearrange the equation to solve for the pressure:

P = (nRT) / V

Since the number of moles of gas remains constant, we can rewrite the equation as:

P1V1 = P2V2

Where: - P1 is the initial pressure of the gas - V1 is the initial volume of the gas - P2 is the final pressure of the gas - V2 is the final volume of the gas

In this problem, we are given the initial pressure P1, initial volume V1, and the final volume V2. We need to find the final pressure P2.

To solve for P2, we can use the equation:

P2 = (P1 * V1) / V2

Let's substitute the given values into the equation and calculate the final pressure P2.

Given: - V1 = 75 L (initial volume) - P1 = 9.9 MPa (initial pressure) - T1 = -9 degrees Celsius (initial temperature) - T2 = 27 degrees Celsius (final temperature)

First, we need to convert the temperatures from Celsius to Kelvin:

T1 (in Kelvin) = T1 (in Celsius) + 273.15 T2 (in Kelvin) = T2 (in Celsius) + 273.15

Substituting the values into the equation:

P2 = (P1 * V1) / V2

P2 = (9.9 MPa * 75 L) / V2

Now, let's calculate the final pressure P2.

Using the given values, we have: - V1 = 75 L - P1 = 9.9 MPa - T1 = -9 degrees Celsius = 264.15 Kelvin - T2 = 27 degrees Celsius = 300.15 Kelvin

Substituting the values into the equation:

P2 = (9.9 MPa * 75 L) / V2

P2 = (9.9 * 75) / V2 MPa

Now, we need to find the final volume V2. Since the volume remains constant, V2 is equal to V1.

Substituting V2 = V1 = 75 L into the equation:

P2 = (9.9 * 75) / 75 MPa

Simplifying the equation:

P2 = 9.9 MPa

Therefore, the pressure of the gas in the cylinder, when transferred to a heated room with a temperature of 27 degrees Celsius, will be 9.9 MPa.

Answer:

The pressure of the gas in the cylinder, when transferred to a heated room with a temperature of 27 degrees Celsius, will be 9.9 MPa.