Consider a piston-cylinder assembly that contains 1mole of idealgas,A. The syste

Question

Consider a piston-cylinder assembly that contains 1mole of idealgas,A. The system is well insulated. Its initial volumeis 10L and intial pressure,2bar. The gas is allowed to expandagainst a constant external pressure of 1bar until it reachesmechanical equilbrium. Is this a reversible process? What is the final temperature of the system? How much workwas obtained? For gas A:cv=(5/2)R

Explanation / Answer

no not reversible process; a reversible process always hasmechanical equilibrium (Pgas = Pext => 2 bar =/= 1bar) dU = Cv*dT = Q + W = 0 + W     (well insulated => no heat flow_ Cv*dT = W = -PdV Cv*T = -Pext*V = Vfinal: Pi *Vi = Pf *Vf          Vf = Vi *(Pi/Pf) = 10 L *(2 bar /1 bar) = 20 L T = -(Pext*V)/Cv = -[1 bar * (20 L - 10L)]*(105 Pa/ 1bar) *(1 atm /101325 Pa) / [ 5*0.0821L*atm/mol-K /2] T = -48.0839594 K Tfinal = Tinitial + T = (Pi*Vi/nR) + T TFinal = (2 bar * 10 L / [1 mol * 0.0821 L*atm/mol-K])*(105 Pa/1bar) *(1atm/ 101325 Pa) + (-48.0839594 K) Tfinal = 192.335897 K Tfianl = 192 K

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