Finding the Volume of an Ideal Gas

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SUMMARY

The discussion centers on calculating the volume of an ideal gas using two different approaches: the ideal gas equation PV=mRT and the density formula Density = Mass/Volume. The correct volume was calculated as 4.305 m² using the ideal gas equation, but the density method yielded 4.08 m³ due to incorrect unit application. Participants clarified that air density varies with temperature and pressure, necessitating the use of given values for accurate calculations. The primary issue identified was the misinterpretation of units, emphasizing the importance of unit consistency in gas volume calculations.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV=mRT)
  • Knowledge of density calculations (Density = Mass/Volume)
  • Familiarity with the concepts of temperature and pressure effects on gas density
  • Basic unit conversion skills in physics
NEXT STEPS
  • Study the Ideal Gas Law and its applications in real-world scenarios
  • Research the effects of temperature and pressure on gas density
  • Learn about unit conversions in physics, particularly in gas calculations
  • Explore common mistakes in gas law calculations and how to avoid them
USEFUL FOR

Students in physics or chemistry, educators teaching gas laws, and professionals involved in fields requiring gas volume calculations, such as meteorology or engineering.

Kajan thana
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Homework Statement
A rigid tank contains 5 kg of air at 100 kPa and 27 °C. The air is now heated until
its pressure doubles. Determine the volume of the air?
Relevant Equations
1) PV= mRT.
2) Denisty = Mass/Volume
Hi,

I tried to do this question in two different approaches one of them was using the equation PV=mRT where I got the right answer which is 4.305 m**2. However, I tried using this Density = Mass/Volume, where I substituted Denisity= 1.225 and Mass equals 5kg to get the volume as 4.08.
Can someone tell me why I can't use the second equation? Is it because the density of the air varies?
 
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Kajan thana said:
Is it because the density of the air varies?
Yes. The density of air will vary with temperature and pressure. You are given values for both and should use those values.

The volume of the air is most definitely not 4.305 m2. Can you see why?
 
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jbriggs444 said:
Yes. The density of air will vary with temperature and pressure. You are given values for both and should use those values.

The volume of the air is most definitely not 4.305 m2. Can you see why?
Thank you.
It makes sense that the density will vary with temperature and pressure so I have to use the values that is given. But can please explain why 4.305m2 is not also the right answer ( according to marking scheme, it is ) ?
 
Last edited:
Hint: the problem is not with the number, but the units.
 
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mjc123 said:
Hint: the problem is not with the number, but the units.
Oh thank you.. Yh wrong unit..
 

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