Work Done by Gas: Ideal Diatomic Process

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SUMMARY

The discussion centers on the work done by a 1.00 mol sample of an ideal diatomic gas during a process where its pressure increases linearly from 1.00 atm at 420 K to 1.60 atm at 720 K. The key equations involved are the ideal gas law (PV = nRT) and the work done equation (W = ∫PdV). Participants clarify that while the number of moles (n) remains constant, the volume (V) must change due to the linear relationship between pressure (P) and temperature (T), indicating heat transfer is also involved in the process.

PREREQUISITES
  • Understanding of the ideal gas law (PV = nRT)
  • Knowledge of thermodynamic processes involving gases
  • Familiarity with calculus concepts, particularly integration for work calculation
  • Basic principles of heat transfer in thermodynamics
NEXT STEPS
  • Study the derivation and application of the ideal gas law in different thermodynamic processes
  • Learn about the relationship between pressure, volume, and temperature in non-ideal gas scenarios
  • Explore the concept of heat transfer and its effects on gas behavior during processes
  • Investigate the mathematical techniques for calculating work done in variable pressure scenarios
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Students studying thermodynamics, physics enthusiasts, and professionals in engineering fields who require a deeper understanding of gas behavior under varying conditions.

Hlud
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Homework Statement


A 1.00 mol sample of an ideal diatomic gas at a pressure of 1.00 atm and temperature of 420 K undergoes a process in which its pressure increases linearly with temperature. The final temperature and pressure are 720 K and 1.60 atm. Determine the work done by this gas during this process.

Homework Equations


PV = nRT and W = int(PdV)

The Attempt at a Solution


So, i checked online for a solution and checked the official solutions manual, after i was stumped for awhile. My biggest issue is that both agree that volume changes. But if P = nR/V *T, and P varies linearly with T, then how is V not a constant? Or if it is changing, then how is n still a constant?
 
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Hlud said:

Homework Statement


A 1.00 mol sample of an ideal diatomic gas at a pressure of 1.00 atm and temperature of 420 K undergoes a process in which its pressure increases linearly with temperature. The final temperature and pressure are 720 K and 1.60 atm. Determine the work done by this gas during this process.

Homework Equations


PV = nRT and W = int(PdV)

The Attempt at a Solution


So, i checked online for a solution and checked the official solutions manual, after i was stumped for awhile. My biggest issue is that both agree that volume changes. But if P = nR/V *T, and P varies linearly with T, then how is V not a constant? Or if it is changing, then how is n still a constant?
It's a 1 mole sample. What does that tell you about n ?
 
If n is constant, then how is V not constant? The slope of the straight line (in this case slope = nR/V) should be constant. If n and R are to be constants, then i assume that V should be constant as well. However, neither solution i have checked show this.
 
Hlud said:
If n is constant, then how is V not constant? The slope of the straight line (in this case slope = nR/V) should be constant. If n and R are to be constants, then i assume that V should be constant as well. However, neither solution i have checked show this.
It must be that there is heat transfer involved as well.
 
I am missing something. If heat is added, can the temperature still vary linearly with pressure? Or is it no longer an ideal gas.
 
SammyS said:
It must be that there is heat transfer involved as well.
That may have been a bit misleading.

The statement says that P varies linearly with T. It does not say that they are proportional.
 
SammyS said:
The statement says that P varies linearly with T. It does not say that they are proportional.

So, there must be a nonzero y-intercept. Thanks, that clears it up!
 
Hlud said:
So, there must be a nonzero y-intercept. Thanks, that clears it up!
Yes. That's the trick.
 

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