Change in entropy in a polytropic process

[ricof]

Homework Statement

A piston cylinder device contains 1.2kg of nitrogen at 120kPa and 300K. Gas is compressed slowly in a polytropic process during which PV^1.3 = constant. The proces ends when the volume is reduced by one half. What is the entropy change?

Homework Equations

(P2/P1) = (V1/V2)^n

The Attempt at a Solution

Assuming V1 = 1 and therefore V2 = 0.5, I have worked out P2 as 295.5kPa but I am stuck on what to do next.

 

[ricof]

I should add that I have absolutely no idea where or how the 1.2kg of nitrogen comes into the equation, nor if V1 is in fact 1.

Please help me I've been staring at this one for hours!

 

[ricof]

anyone?

 

[Mapes]

How many moles is 1.2kg of nitrogen?

 

[Redbelly98]

Homework Statement

A piston cylinder device contains 1.2kg of nitrogen at 120kPa and 300K. Gas is compressed slowly in a polytropic process during which PV^1.3 = constant. The proces ends when the volume is reduced by one half. What is the entropy change?

Homework Equations

(P2/P1) = (V1/V2)^n

The Attempt at a Solution

Assuming V1 = 1 and therefore V2 = 0.5, I have worked out P2 as 295.5kPa but I am stuck on what to do next.

I should add that I have absolutely no idea where or how the 1.2kg of nitrogen comes into the equation, nor if V1 is in fact 1.

You can get V1 from the ideal gas equation. The 1.2 kg will come in handy there.

For entropy change, a useful relation is dQ/T = dS.

 

[ricof]

Oh right ok so

120kPa x V = 1.2 x R x 300K

As the gas is Nitrogen do I still use R=8.314?

 

[Redbelly98]

Oh right ok so

120kPa x V = 1.2 x R x 300K

This looks wrong. Where does this equation come from, and what does the 1.2 represent here? Include units with all quantities, and ask yourself if the units are what the should be.

As the gas is Nitrogen do I still use R=8.314?

No, use R = 8.314 Pa*m^3 / (mole*K). "8.314" is not the same thing.

 

[ricof]

In your previous post you mentioned the ideal gas law which is PV=nRT no?

n is the number of moles so I think you use the mass of the nitrogen (1.2kg) in there somewhere?

 

[Redbelly98]

Yes, you use PV = nRT.

n is the number of moles of nitrogen, not the mass of nitrogen. You have to figure out how many moles there are. See Mapes's post #4

 

[ricof]

The atomic weight of nitrogen is 7 but as it is diatomic, the molecular weight is 7x2 = 14.

So 1.2kgs represents 1200/14= 85.7 moles = n?

 

[Redbelly98]

That's the right idea, but you should look up the atomic weight of nitrogen.

 

[ricof]

Thanks, have now got the answer