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

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SUMMARY

This discussion focuses on calculating pressure in a heated closed system vessel containing argon gas. The ideal gas law, represented by the equation PV=nRT, is utilized to determine the relationship between pressure (P), volume (V), and temperature (T). The user successfully calculates the final pressure at 500°C (773K) using the density of argon at standard temperature and pressure (STP), resulting in a pressure of approximately 232.2 kPa (2.29 atm). The discussion emphasizes that in a closed system, the volume remains constant, and thus the pressure is directly proportional to temperature.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV=nRT)
  • Knowledge of gas properties, specifically for argon
  • Familiarity with density calculations (density=m/V)
  • Basic thermodynamics concepts related to closed systems
NEXT STEPS
  • Research the Van der Waals equation for real gas behavior
  • Study the impact of temperature on gas density and its implications
  • Explore safety factors in high-temperature gas systems
  • Learn about the specific heat capacities of argon and their relevance in thermal calculations
USEFUL FOR

Engineering students, chemical engineers, and professionals involved in thermodynamics and gas system design will benefit from this discussion, particularly those focusing on pressure calculations in closed systems.

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

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