Calculating Heat & Work for 1 Mole of Ideal Gas

[kalbuskj31]

Homework Statement

1 mole of monatomic ideal gas. P1 = 2 atm V1 = 44.8 L T1 = 1092 K. The path to P2 = 1 atm V2 = 22.4 L and T2 = 273K is P = 6.643E-4 * V^2 + 2/3. Calculate the heat and work.

Homework Equations

q = nCpΔT
w = PΔV

The Attempt at a Solution

I attempted to directly plug in the data that was available and didn't work. Neither P,V, or T are constants during this state change. I just realized in posting this problem I'm not sure what equation to use since every variable is changing. Suggestions?

q = -13.5kJ w = -3278 J

 

[vela]

You need to use the more general definition of work:

$$W=\int P\,dV$$

You'll also want to use the first law to solve the problem.

 

[kalbuskj31]

I was able to find work by figuring out the area under the curve.

The solution that I found for q baffles me. This question was the last part of a series of state changes in a cyclic reaction. I found the answer by adding the q and subtracting w from the previous parts of the problem. That shouldn't work like that right?

 

[Andrew Mason]

I was able to find work by figuring out the area under the curve.

The solution that I found for q baffles me. This question was the last part of a series of state changes in a cyclic reaction. I found the answer by adding the q and subtracting w from the previous parts of the problem. That shouldn't work like that right?

You are given the change in temperature so you can easily determine $\Delta U$. You have figured out the work done. So apply the first law to find heat flow:

$$\Delta Q = \Delta U + W$$

AM

 

[Mindscrape]

I suggest memorizing now these two formulas

dU = dW + dQ (for work done on the environment)
dW = d(pV)

 

[Andrew Mason]

I suggest memorizing now these two formulas

dU = dW + dQ (for work done on the environment)
dW = d(pV)

Except that it should be dQ = dU + dW then, where dW is the work done BY the gas/system (ie. ON the surroundings).

AM

 

[kalbuskj31]

Thanks, I did some alegbra incorrectly and stumbled across something that I found very very unusual. Is it safe to assume what I found is a rare coincidence?

 

[Andrew Mason]

Thanks, I did some alegbra incorrectly and stumbled across something that I found very very unusual. Is it safe to assume what I found is a rare coincidence?

I am not sure what you did. Your formula for dq = nCpdT is incorrect, since this is not a constant P process. You determine dQ by finding the work done (by integrating PdV (substituting the given formula for P) and the change in U (using change in temperature) and then applying the first law.

AM

 

[Mindscrape]

Ah, my bad, I got the sign convention wrong. I hate that thing. I should have looked it up. :(

Anyway, my advice still holds, memorize those formulas and learn how to use them because you'll see more as you go through thermo.

Oh yeah, and also kalbuskj, mistakes are invaluable. Sometimes you'll learn more than you ever could in getting the problem wrong and figuring out why it is wrong then getting it right to begin with. Don't just work the problem with the goal of getting it right, work it with the goal of finding your misconception, fixing it, and reworking the problem with the right concepts.