thermodynamics quiestion

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one kilogram air contained in piston cylinder assembly,initially at 6 bar and 400 K, undergoes an expansion to a final temperature of 300 K during which the pressure volume realtionship is pv^1.3=constant. assuming air behaves like an ideal gas determine 

a. the final pressure in bar 

b. the work in kJ 

c. the heat transfer in kJ

Oct 1st, 2015

Thank you for the opportunity to help you with your question!

a. final presure

given pv^1.3=constant

we know that pv=mRT for ideal gas where m is mass, R is universal gas constant and T is temperature

we can find the initial volume 1 as p1v1=mRT1

v1=(1*0.287*400/6)=19.133

from p1v1^1.3=constant

v2=0.3 root(v1^1.3*p1/(mRT2))=49.9.

p2=mRT2/v2=1.7249 bar (final presure)

b, work done w=(p2v2-p1v1)/n-1

n=1.3

therefore, w=95.74kJ

c the heat transfer

Q=change in u-work done

change in u=cv(T2-T1)

cv for air = 0.717

u=71.7

Q=71.7+95.7=167.4kJ

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 1st, 2015

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