Thermodynamics piston–cylinder assembly Question

[derrickb]

Homework Statement

A piston–cylinder assembly contains air, initially at 2 bar, 300 K, and a volume of 2 m3. The air undergoes a process to a state where the pressure is 1 bar, during which the pressure–volume relationship is pV 5 constant. Assuming ideal gas behavior for the air, determine the mass of the air, in kg, and the work and heat transfer, each in kJ.

Homework Equations

Pv=RT, v=specific volume
W=$\int$PdV
Q-W=ΔE

The Attempt at a Solution

Pv=RT
(2 bar)(100 kPa/bar)v=(.286)(300 K)
v=0.429 m³/kg

v=V/m
m=V/v
m=2 m³/0.429 m³/kg
m=4.66kg

I feel like this may be incorrect.

W=$\int$PdV
Would W=0 because PV is constant?

I'm kind of lost at this point. If anyone could point me in the right direction, I would really appreciate it

 

[rude man]

Homework Statement

A piston–cylinder assembly contains air, initially at 2 bar, 300 K, and a volume of 2 m3. The air undergoes a process to a state where the pressure is 1 bar, during which the pressure–volume relationship is pV 5 constant. Assuming ideal gas behavior for the air, determine the mass of the air, in kg, and the work and heat transfer, each in kJ.

Homework Equations

Pv=RT, v=specific volume

You're not necessarily dealing with 1 kg of air. So your formula should be
pV =mR_specificT, V = actual volume, m= actual mass, p in Pascals. 1 Pascal ~ 1e-5 bar.

R_specific for air is 287 J kg^-1 K^-1 so where did you get 0.286? Are you using SI units thruout I hope?

 

[derrickb]

You're not necessarily dealing with 1 kg of air. So your formula should be
pV =mR_specificT, V = actual volume, m= actual mass, p in Pascals. 1 Pascal ~ 1e-5 bar.

Technically, the formula you put is the same as mine, I just divided V by m to get a separate variable v. That formula shouldn't only apply to 1 kg of air. In the steps after, I substituted V/m in for v and solved for m. There isn't anything wrong with this; I guess it's just the longer way of doing it. As for units, I thought that I had them correct. Maybe the .286 is kJ/kgK? I'm not really sure

 

[rude man]

As for units, I thought that I had them correct. Maybe the .286 is kJ/kgK? I'm not really sure

Yes, that would account for your being off by a factor of 1000.

You need to stick to SI units. The SI unit is the Joule, not kilojoule.

 

[derrickb]

Ok I'll make sure to watch units. The answer I got for mass wouldn't change, the decimal place will just move. Can anyone help with the work part of the problem? Would work be 0 because pV remains constant?

 

[rude man]

Ok I'll make sure to watch units. The answer I got for mass wouldn't change, the decimal place will just move. Can anyone help with the work part of the problem? Would work be 0 because pV remains constant?

Work = ∫pdV.
pV^0.5 = cosntant.

Since you're told p changes, then so must V. And if V changes, work will be done either on or by the system.

 

[Chestermiller]

To expand on what rude man said, there is also a temperature change during the expansion. That is how the pressure and volume are controlled to satisfy pv^0.5 = const. Use rude man's equations of the previous post to calculate the amount of work done. Tell us what you get.

Chet

 

[derrickb]

I don't understand why there would be a temperature change in this problem. It says pV as a whole remains constant, but the values of p and V change. If pV is constant, mRT remains constant and, assuming there isn't a change in mass, the temperature remains the same. I finished the problem and got a mass=4.65kg, W=277.2kJ, and Q=277.2kJ. If T remains constant, Q must equal W because ΔE=0.

 

[rude man]

I don't understand why there would be a temperature change in this problem. It says pV as a whole remains constant, but the values of p and V change. If pV is constant, mRT remains constant and, assuming there isn't a change in mass, the temperature remains the same. I finished the problem and got a mass=4.65kg, W=277.2kJ, and Q=277.2kJ. If T remains constant, Q must equal W because ΔE=0.

It does not say pV remains constant. I think it says pV^0.5 remains constant. So T changes.

Your answers are correspondingly wrong.

I have to admit that the statement as you posted it is questionable. Could you dig up the original for us?

 

[derrickb]

Yeah I just reread the question statement that I posted and it must have changed when I copy and pasted it from the pdf of the book. Instead of pV 5 constant, it says pV=constant. Sorry for all the confusion.

 

[rude man]

Yeah I just reread the question statement that I posted and it must have changed when I copy and pasted it from the pdf of the book. Instead of pV 5 constant, it says pV=constant. Sorry for all the confusion.

OK, so temperature does remain constant.

But work is still not zero.

 

[derrickb]

YEah I figured out how to solve for work and my answer was 277.2 kJ I believe.

 

[rude man]

YEah I figured out how to solve for work and my answer was 277.2 kJ I believe.

That answer is correct if you computed the mass right, which I did not check.