Question

В сосуде находится газ под давлением 0,60 МПа. Какие установится давление, если из сосуда выпустить 3/8 содежащегося там газа? Температуру считать постоянной.

Answer 1

Из уравнения Менделеева-Клайперона

 PV=m/µ *RT

 

Состояние 1

 

P1V=m1/µ *RT

P1/m1 =RT / ( µ V)  (1)

 

Состояние  2

 

P2/m2 =RT / ( µ V)  (2)

 

Температуру считать постоянной – объем тоже не менялся

Тогда правые части (1) и (2) равны

Можно приравнять левые части

 

P1/m1= P2/m2

Р1/Р2 = m1/m2

 

По условию m2=m1-3/8m1=5/8m1

Тогда

Р1/Р2 = m1/m2=m1 / (5/8m1)=8/5

 

P2=5/8P1= 5/8 *0,60 МПа=   0,375 МПа = 375 кПа = 375000 Па

 

Ответ  0,375 МПа = 375 кПа = 375000 Па

Answer 2

Calculating Pressure Change After Releasing Gas

To calculate the pressure change after releasing 3/8 of the gas from the vessel, we can use the ideal gas law formula, which states that 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, and - T is the temperature of the gas.

Given that the temperature is constant, we can use the formula p1V1 = p2V2 to find the final pressure (p2) after releasing 3/8 of the gas.

Applying the Ideal Gas Law

Let's denote the initial pressure as p1 and the initial volume as V1. After releasing 3/8 of the gas, the remaining volume will be V2 = (5/8)V1.

Using the formula p1V1 = p2V2, we can solve for p2:

p1V1 = p2V2 p1V1 = p2(5/8)V1 p2 = (8/5)p1

Calculating the Final Pressure

Given the initial pressure p1 = 0.60 MPa, we can calculate the final pressure p2:

p2 = (8/5) * 0.60 MPa p2 = 0.96 MPa

So, the pressure after releasing 3/8 of the gas will be 0.96 MPa.

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