# Work done by a Gas

## 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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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 ?

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
Staff Emeritus
Homework Helper
Gold Member
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
Staff Emeritus
Homework Helper
Gold Member
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.

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
Staff Emeritus