How Do You Calculate Pressure in a Heated Closed System Vessel?

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In summary, the conversation discusses an analysis on a closed system vessel that will be heated up for an experiment. The main equations used are PV=nRT and density=m/V. The volume and number of moles are constant, making the relation between pressure and temperature directly proportional. The question of using the density of argon at STP (1 atm and 25C) for a higher temperature (500C) is also addressed.
  • #1
alex-book
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Homework Statement



Hi I am an Engineering student and i have to do an analysis on a closed system vessel that is going to be heated up.And before i start the experiment i want to an analysis or a safety factor for this experiment.

I am going to have a closed system vessel, let's say the volume is going to be 3 m^3. and surface area of 3m^2.
Initially i am going to put an argon gas inside the closed vessel when the vessel is still at room temperature (25C) and then heat it up until it reach 500Celsius.(T=773K)



Homework Equations



Pv=nRT, and density=m/V

The Attempt at a Solution



and gas volume is always the same with the medium right? so the argon gas volume on a 3m^3 vessel will be 3m^3 as well right?

but isn't it that the volume of the gas depends on the temperature and the pressure?

or can i just calculate the mass by using the density of the argon gas at 25C and find the mass or the mass is going to be different at 500C?

Sorry about a lot of confusion in my posting, i am really confused and do need help. Thank you
 
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  • #2
alex-book said:
I am going to have a closed system vessel, let's say the volume is going to be 3 m^3. and surface area of 3m^2.
Actually a 3 m^3 volume must have a surface area of at least 10 m^2, but that isn't really important for this problem.

Initially i am going to put an argon gas inside the closed vessel when the vessel is still at room temperature (25C) and then heat it up until it reach 500Celsius.(T=773K)

Homework Equations



Pv=nRT, and density=m/V

The Attempt at a Solution



and gas volume is always the same with the medium right? so the argon gas volume on a 3m^3 vessel will be 3m^3 as well right?
Yes.
but isn't it that the volume of the gas depends on the temperature and the pressure?
Those 3 are all related to each other, through PV=nRT.

Since V is a constant (in this situation), what can you say about the ratio P/T?

p.s welcome to PF :smile:
 
  • #3
Redbelly98 said:
Actually a 3 m^3 volume must have a surface area of at least 10 m^2, but that isn't really important for this problem.


Yes.

Those 3 are all related to each other, through PV=nRT.

Since V is a constant (in this situation), what can you say about the ratio P/T?

p.s welcome to PF :smile:

Thnx redbelly98!

ohhh so the volume stays the same? well :) i kno its a stupid question, its just that the volume tend to increase with the temperature right?
And it is true right for Argon gas i can just use ideal gas equation, or should i go with the non-ideal gas formula?

Thanks again!
 
  • #4
At room temperature and 1 atm pressure, argon is close to an ideal gas.

To calculate the final pressure, you can try both ideal and real gas solutions and compare them.

Since n/V is fixed, and can be calculated at room temp & 1 atm, the real gas calculation is not as complicated as you might think.
 
  • #5
Redbelly98 said:
At room temperature and 1 atm pressure, argon is close to an ideal gas.

To calculate the final pressure, you can try both ideal and real gas solutions and compare them.

Since n/V is fixed, and can be calculated at room temp & 1 atm, the real gas calculation is not as complicated as you might think.

Yea i have tried both real gas and ideal gas equation and both of them almost the same, took me so long to find the van der waals constant+equation. Thanks Redbelly!
and for both of calculation i used the density of argon at STP(1atm and 25C) which is 1.449kg/m3 is that okay?

so it will be like this

PV=nRT --> n = m/M and Rspecific = R/M so PV=mRspecific T --> P = density*Rspecific*T

so P = density * Rspecific * Temp
= 1.449 kg/m3 *0.208 KJ/kgK *773K
= 232.2 KPa = 2.29 atm (I have tried to calculate it using Vdwaals equation and it got me almost the same result. )

is that correct?
but it is just weird to use the density of STP value to calculate in 500C temperature. Because i know in h2O there is different value of density that you have to use in different type of temperature and pressure, this confuses me, like do i need to find the exact value of density of argon at 500C or i can just use the SPT one?
but in the other hand density is mass/volume and in this case mass and volume stays the same since its a closed vessel, so may be i could use the same density value, is that the reason?
I am sorry if i confuse you with my 100000questions, is just that i want to learn+do this right :) Please help&enlighten me..Thanks again Redbelly! :)
 
Last edited:
  • #6
You're making it more complicated than necessary.

PV = nRT

Volume and # of moles are constant. So what is the relation between P and T?
 
  • #7
Redbelly98 said:
You're making it more complicated than necessary.

PV = nRT

Volume and # of moles are constant. So what is the relation between P and T?

directly proportional?
k thanks redbelly! i think i got it! thnx
 
  • #8
alex-book said:
directly proportional?
Yes, exactly.
k thanks redbelly! i think i got it! thnx
You're welcome :smile:
 

FAQ: How Do You Calculate Pressure in a Heated Closed System Vessel?

What is pressure and how is it measured?

Pressure is defined as the amount of force exerted per unit area. It is typically measured in units of pascals (Pa) or pounds per square inch (psi). Pressure can be measured using a variety of instruments, such as a manometer, barometer, or pressure gauge.

What factors affect pressure?

The main factors that affect pressure are the amount of force applied and the size of the area over which the force is distributed. Other factors that can impact pressure include the temperature, type of material, and altitude.

How do you calculate pressure?

Pressure can be calculated using the formula P = F/A, where P is pressure, F is force, and A is area. It is important to ensure that the units of force and area are consistent in order to get an accurate result.

Can pressure be negative?

Yes, pressure can be negative. Negative pressure, also known as vacuum or suction, occurs when the force is pulling inwards instead of pushing outwards. It is commonly observed in situations such as a plunger pulling water out of a clogged drain or a vacuum cleaner sucking up dirt.

How is pressure used in everyday life?

Pressure is used in many everyday applications, such as in car tires, blood pressure measurements, and scuba diving. It is also important in weather forecasting, as changes in air pressure can indicate changes in the weather. In addition, pressure plays a crucial role in engineering and construction, as it helps determine the strength and stability of structures.

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