I don't believe I'm getting the correct answers for this problem. Could someone look over my work and verify whether it is correct or not?
One mole of an ideal gas (Cv = 3/2R) at 300. K expands adiabatically against a constant external pressure of 2.00 atm from a volume of 1.00 L to 5.00 L. Find delta-S gas, delta-S surroundings, delta-S universe for the process.
my work:
P1 = nRT/V
P1= (1.00 mol * .08206 * 300. K)/1.00 L= 24.6 atm
P2= P1(V1/V2)^Cp/Cv
P2= 24.6 atm(1.00 L/5.00 L)^5/3 = 1.68 atm
T2= PV/nR
T2= (1.68 atm * 5.00 L)/(1.00 mol * .08206)= 102.5 K
delta-S g= nRlnT2/T1 + nRlnV2/V1
delta-S g= 1.00 mol*(3/2*8.314 J/mol K)*ln(102.5K/300.K) + 1.00 mol*(8.314 J/mol K)*ln(5.00L/1.00L) = -.0120 J/K
delta-S surr= -q/T
but q=0 so delta-S surr= 0
delta-S univ= delta-S surr + delta-S gas
delta-S univ= -.0120 J/K
I noticed that I never used the external pressure given in the problem. Something is telling me that it was given for a reason. Where should I have used it? Also, is the equation for delta-S surr correct? I'm not sure if it's limited to certain situations.
1 answer