[Humanities]

One mole of a monatomic ideal gas begins in a state with P = 1.00 atm and T = 303 K. It is expanded reversibly and adiabatically until the volume has increased by a factor of 2.42; then it is expanded irreversibly and isothermally into a vacuum until the volume has been increased by a factor of 2.42 again; then it is heated reversibly at constant volume to 453 K. Finally, it is compressed reversibly and isothermally until a final state with P = 1.00 atm and T = 453 K is reached. Calculate ΔSsys for this process. (Hint: There are two ways to solve this problem — an easy way and a hard way.)

1.) Reversible adiabatic expansion:   ΔS1 = 0.000 J K-1

2.) Irreversible isothermal expansion:   ΔS2 = 7.35 J K-1

3.) Reversible heating at constant V:   ΔS3 = ?

4.) Reversible isothermal compression:   ΔS4 = ?

     Overall process:   ΔS = 8.36 J K-1



I need help with steps three and four...The first part is 0 because it's adiabatic, the second part i used nR(ln(V2/V1), and the total i used the monatomic constant 5/2(8.315)(ln(T2/T1)) because there's 0 net pressure change...I'm not sure what to do for parts 3 and 4, i keep getting them wrong.  Thanks!