0.410 mol f a monatomic gas fills a 1 dm^3 container to a pressure of 1.0133 MPa. It’s a expanded reversibly and adiabatically until a pressure of 0.101 33 MPa is reached. What are the final volume and temperature? What is the work done in the expansion?   ​

Dear student
Please find the solution to the asked query: 
The final volume vf of the gas after adiabatic and reversible expansion can be obtained using the expression:
piViγ = pfVfγSubstituting the values of pi, Vi, pf, and γwe get:(1.0133MPa)(1dm3)5/3 =(0.10133MPa)Vf5/3 thus Vf = 103/5dm3 = 3.98dm3The final temperature Tf after the expansion is:Tf =pfVfnR=(0.10133×103kPa)(3.98dm3)(0.410mol)(8.314dm3kPamol-1K-1)                  =118.3 KThe work done during expansion is w =-piVi- pfVfγ-1=-(1.013MPa)(1dm3)-(0.10133MPa)(3.98dm3)(5/3)-1    =-0.915dm3 MPa = -915J
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