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Work done by a Gas

  • Thread starter Hlud
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  • #1
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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?
 

Answers and Replies

  • #2
SammyS
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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?
It's a 1 mole sample. What does that tell you about n ?
 
  • #3
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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.
 
  • #4
SammyS
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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.
 
  • #5
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I am missing something. If heat is added, can the temperature still vary linearly with pressure? Or is it no longer an ideal gas.
 
  • #6
SammyS
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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.
 
  • #7
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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!
 
  • #8
SammyS
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So, there must be a nonzero y-intercept. Thanks, that clears it up!
Yes. That's the trick.
 

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