Thermodynamics -- calculating fluid mass

[BurningUrge]

This is quite possibly very basic, but I have a horrible habit of forgetting basics as I move up the ladder in difficulty during the semester. This is a question regarding Thermodynamics, taken from Chapter 1; Introduction and the First Law of Thermodynamics of the book Applied Thermodynamics for Engineering Technologist (5th Edition).

I am including the whole question just to avoid any misunderstandings.

Homework Statement

A fluid at 0.7 bar occupying 0.09m³ is compressed reversibly to a pressure of 3.5 bar according to law pvⁿ = constant. The fluid is then heated reversibly at constant volume until the pressure is 4 bar; the spesific volume is then 0.05m³ / kg. A reversible expansion according to a law pv² = constant restores the fluid to its initial state. Sketch the cycle to a p-v diagram and calculate:

i) The mass of fluid present (THIS is the one I cannot seem to figure out.. basics be damned)
ii) the value of n in the first process.
iii) the net work of the cycle.

Homework Equations

It is a fluid, not explicitly stated to be gas or liquid, so the basic pv = nRT doesn't necessarily apply here.

The Attempt at a Solution

I'm stumped, really. I have the answer (0.0753 kg) but I cannot figure out how to get to it.

 

[DrClaude]

Sketch the cycle to a p-v diagram and calculate:

Did you do that?

To get the mass, you will need to use the specific volume given.

 

[DrClaude]

I have the answer (0.0753 kg) but I cannot figure out how to get to it.

I just calculated it myself, and I'm off by a factor of 10. Could you please check all the numerical values you have given in the problem?

 

[BurningUrge]

Okay, so I rechecked the values, and the Spesific volume is meant to be 0.5, NOT 0.05. One slight tap too much on the 0 there.

Also, I did sketch the p-v diagram, yes. I'm pretty sure I got the understanding of how the process looks.

And when you say that I need to use Spesific volume, it strikes me how stupid I have actually been trying to figure this out. With that in mind, which formula would you suggest looking into for calculating the mass when I don't actually have the current volume? It's a pvⁿ = constant, so I can't figure it out with the p₁V₁ = p₂V₂

 

[DrClaude]

Okay, so I rechecked the values, and the Spesific volume is meant to be 0.5, NOT 0.05. One slight tap too much on the 0 there.

Good, then I get the correct result.

Also, I did sketch the p-v diagram, yes. I'm pretty sure I got the understanding of how the process looks.

Then you should see that there are two processes that link the initial state to the unknown volume.

 

[BurningUrge]

Then you should see that there are two processes that link the initial state to the unknown volume.

Yes there is. The 1 -> 2 and 3 ->4 both link the process from the initial volume to the unknown. Does it have anything to do with the pv² = constant that is the exponent for the revesible process happening in 3 -> 4?

Or put in this way, I can figure out the volume using p₁V₁² = p₃V₃², where V₃ = V₂

 

[DrClaude]

Or put in this way, I can figure out the volume using p₁V₁² = p₃V₃²

Correct.

 

[BurningUrge]

Then I have my answer and I am greatly appreciative of your help. Thank you very much!