Work Done by Gas: Ideal Diatomic Process

[Hlud]

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?

 

[SammyS]

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 ?

 

[Hlud]

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.

 

[SammyS]

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.

 

[Hlud]

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]

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.

 

[Hlud]

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!

 

[SammyS]

So, there must be a nonzero y-intercept. Thanks, that clears it up!

Yes. That's the trick.