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A
awibroe1-Visitor
1-Visitor
September 20, 2017
Question

Thermodynamic Problem

  • September 20, 2017
  • 2 replies
  • 6736 views

Hello to all,

 

I am having another 'simple' moment where I am going round in circles and am starting to feel a bit dim.

 

In the attached is a simple thermo question I am trying to complete.

 

I have completed a-c with some ease but am struggling with d. where the hint is to evaluate the integral of pressure over dVolume in the associated Pressure/Volume graph. 

 

I know that the integral of an isothermal expansion is either P*V*In(r) = heat supplied or m*R*T*In(r)

 

Where P and V are the initial (Pre-expansion) Pressure and Volume respectively and r is the ratio of expansion i.e. V2/V1. m being mass and R being the gass constant. 

 

As all figures given are specific i.e. no mass of air is specified I don't beleive I can use mRTIn(r) but cannot evaluate PVIn(r) as I don't know what the initial volume is...

 

I know that the heat supplied (well my calculations beleive it is) 187.5 kJ/kg. 

 

I beleive the approach is to calculate the volumes from the integral and then with this to find the pressure noting PV/T = Constant. 

 

Any help, as always, really appreciated.

 

Andy

2 replies

A
awibroe1-VisitorAuthor
1-Visitor
September 20, 2017

Sorry I should have added:

 

P1 = 800 kN/m^2

T1 = 750 K

R = 0.287kJ/kgK

A
awibroe1-VisitorAuthor
1-Visitor
September 20, 2017

And I am obviously trying to find P2 and to do that beleive I need V1 and V2.

A
awibroe1-VisitorAuthor
1-Visitor
September 20, 2017

So after some further thought, I have an approach but would appreciate someone wiser than I validating this approach...

 

Noting that I have the heat input to the isothermal expansion which is in kJ/kg I have negated m (kg) from the integral mRTIn(r) which would give a result in kJ/kg which is what I am after.

 

Then I can manipulate RTIn(r) to isolate In(r). Then by evaluating e to the power of the result of In(r) should give me r i.e. the expansion ratio i.e. V2/V1. This should then be an identity with P1/P2 noting P1*P2 = V1*V2 and I can then isolate P2 noting I have P1.

 

Any thoughts?

 

A

V
ValeryOchkov24-Ruby IV
24-Ruby IV
September 20, 2017

May be one example with Otto cycle help you

29-3-Otto-numerical.png29-1-Otto-plot.png

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