Answer:
Isothermal : P2 = ( P1V1 / V2 ) , work-done [tex]pdv = nRT * In( \frac{V2}{v1} )[/tex]
Adiabatic : : P2 = [tex]\frac{P1V1^{\frac{5}{3} } }{V2^{\frac{5}{3} } }[/tex] , work-done =
W = [tex](3/2)nR(T1V1^(2/3)/(V2^(2/3)) - T1)[/tex]
Explanation:
initial temperature : T
Pressure : P
initial volume : V1
Final volume : V2
A) If expansion was isothermal calculate final pressure and work-done
we use the gas laws
= PIVI = P2V2
Hence : P2 = ( P1V1 / V2 )
work-done :
[tex]pdv = nRT * In( \frac{V2}{v1} )[/tex]
B) If the expansion was Adiabatic show the Final pressure and work-done
final pressure
[tex]P1V1^y = P2V2^y[/tex]
where y = 5/3
hence : P2 = [tex]\frac{P1V1^{\frac{5}{3} } }{V2^{\frac{5}{3} } }[/tex]
Work-done
W = [tex](3/2)nR(T1V1^(2/3)/(V2^(2/3)) - T1)[/tex]
Where [tex]T2 = T1V1^(2/3)/V2^(2/3)[/tex]
