Question

Сосуд объемом 12л содержащий газ при давлении 400 кПа соединяют с другим сосудом объемом 3л из которого полностью откачан воздух. Найти конечное значение давления. Процесс изотермический.

Answer 1

Дано   P1=400 кПа   V1=12л    V2=3 л       P- ?
так как температура газа не меняется
P1*V1= P(V1+V2)
P= P1*V1/(V1+V2)=400*12/15=320 к Па

Answer 2

Problem Analysis

We are given two vessels: one with a volume of 12 liters containing gas at a pressure of 400 kPa, and another vessel with a volume of 3 liters from which all the air has been completely evacuated. The process is described as isothermal. We need to find the final value of the pressure.

Solution

To solve this problem, we can use the ideal gas law, which states that for an ideal gas, the product of pressure and volume is directly proportional to the product of the number of moles and the temperature. Mathematically, it can be expressed as:

PV = nRT

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

Since the process is described as isothermal, the temperature remains constant. Therefore, we can rewrite the equation as:

P1V1 = P2V2

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

In this case, we know the initial pressure (400 kPa) and volume (12 liters) of the first vessel, and the final volume (3 liters) of the second vessel. We need to find the final pressure (P2).

Using the equation above, we can rearrange it to solve for P2:

P2 = (P1 * V1) / V2

Substituting the given values:

P2 = (400 kPa * 12 L) / 3 L

Now we can calculate the final pressure.

Calculation

Let's calculate the final pressure using the given values:

P2 = (400 kPa * 12 L) / 3 L

P2 = 1600 kPa

Therefore, the final value of the pressure is 1600 kPa.

Answer

The final value of the pressure in the second vessel, connected to the first vessel with a volume of 12 liters containing gas at a pressure of 400 kPa, is 1600 kPa.