Question

7.) One mole of an ideal gas is contained in an insulated piston-cylinder arrangement in an initial state T, P,V. The gas is allowed to expand adiabatically and irreversibly against a constant external pressure P. until a point is reached where the internal pressure becomes equal to Po. If C for the gas is constant and equal to 1.5 R, derive an expression giving the final temperature of the gas in terms of P., V, T, and R.

Answer 1

For adiabetic expansion heat energy or released is zero.

Civen Anuol ideal gas no Tathl Conditions P, T& empanded adiabetically Gas in a Conatant exteral preure binevruatdy and the After internal preoune bome ime Givena15] Cp- Cu R we lenowthat then [Gp 25R] for adiabetic enpansien 40-0 from dirat law A0t AW = CU-intenal enengy then now in epand ant a Conatant eaternal Preraure Po now B0 ideat jan for -aA heat capaaly 40 十Tdv lohere T is Temperalere Cv is is internal Prepune Cue ea 3 4 now

- dv = CudT + T-Po (intenal prenue) 7Tdv we faRd-faeT T2 Cv V2 -26 dv T C CTa-T) alo(Va-y we have from ideat gaeyuation Pv DRT 11 RT2 Po RT2 P2 then V2 1 om C CTa-7) (- RT2 Po RT -20 To TI + CV now +1.5 3.5xT= 1.5 + RT T2 1 3.5 the dral tenperatine is H1erce 3T7 + T2 75

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