# One mole of an Ideal Gas with Cv,m= 5R/2 undergoea...

One mole of an Ideal Gas with Cv,m= 5R/2 undergoea the transformations described inthe following list from an initial state described by T= 250K andP=1.00 bar. Calculate q, w, delta U, delta H, and delta S for eachprocess.

a. The gas undergoes a reversible adiabatic expansion until thefinal pressure is half its initial value.
b. The gas undergoes an adiabatic expansion against a constantexternal pressure of 0.500 bar until the final pressure is half itsinitial value.
c. The gas undergoes an expansion against a constant externalpressure of zero bar until the final pressure is equal to half ofits initial value.
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## Answers ( 2 )

1.
a) For an adiabatic reversal process
heat transfer is zero that is q = 0
W = Cv?T
where Tf =Ti (Pf/Pi)1-1/?
?  U =Wad
? H =  ? U+ nRT
for a reversible process ?S iszero, ?S surr for an adiabatic process is0
b) q = 0
W = Pext  ?V
?  U = Wad
? H =  ? U+ nRT
?S surr for an adiabaticprocess is 0
but ?S sys =CplnT2/T1 + nRlnP1/P2
c). W = 0
q = Cv?T
U = q
? H =  ? U + nRT
?S sys =CplnT2/T1 + nRlnP1/P2
Hope this helps!
2. I have provided the correct formula plz do the problemstepwise and follow the method properly as i have myself cheked itis Tf < Ti
Ur correct that the final temperature in case of anadiabatic process is less than the initial temperature
Tf = TI(Pf / Pi)1-1/?
where? = 1 + R / Cv,m
Ti = 250K , Pf = 1.01atm/2 , Pi = 1.01atm as 1bar= 1.01 atm
Hope this time it will be correct , go throughthe procedure and plz let me know if u have further problem!