Question

1. A sample of 1.00 mol of an ideal gas at 27oC and 1.00 atm is expanded adiabatically and reversibly to 0.50 atm. Determine the values of T_f, q, w, deltaU, deltaH, deltaS, deltaG, deltaS_surr and deltaS_tot. Take Cv = 3/2 R.

Answer 1

For adiabatic process Q= 0 , n= number of moles of ideal gas=1

For adiabatic process (T2/T1)= (P2/P1) ^R/CP

T2= (27+273.15)*(0.5/1) ^2/5 =227.47K

W =delU= nCV*(T2-T1)= 1*1.5*8.315* (227.4-300.15)=-906.392 joules

Cp =CV+R= 5/2R

delH= nCpDelT= 1*2.5*8.314*(227.4-300.15)=-1512.11 Joules

delS= nCP*ln(227.47/300.15)- 1*Rln(0.5/1)= 1*2.5*8.314*ln(227.47/300.15)-8.314*ln(0.5)=0

delG= delH- TdelS= delH= -1512.11 joules

entropy of surroundings= 0

Reversible adiabatic is isentropic process