In: Chemistry
Estimate the final temperature in C when 2.34 moles of oxygen gas is isenthalpically expanded to 10 times its initital volume, starting at standard conditions, which in this case is 298K and 1atm. I know the Joule-Thomson coeffecient for oxygen under these conditions is 0.31Katm^-1.
given moles of gas = 2.4, T= 298K, P=1 atm, V = volume at standard conditions = nRT/P = 2.4*0.0821*298/1= 58.72 L, the volume is expaned to 10 times the orginal volume, New volume, V2= 587.2L
From gas law, Pressure after expansion= nRT/V= 2.4*0.0821*T/582.7 L=0.000338T
for isoenthalpic expansion
(dT/dP)H= joules thomson coefficient = 0.31
dT =0.31* (1-0.000338T)
dT/ (1-0.000338T)=0.31
when integrated between T1= 298K and T2 =final temperature
-ln(1-.000338T2/(1-0.000338T1)= 0.31*0.000338
-ln(1-0.000338T2)/(1-0.000338*298)= 0.000105
(1-0.000338T2)/(1-.000338*298)= 0.9989
1-0.000338T2= 0.8992
T2= 265.3K