Question

Consider an insulated container of volume V2. N ideal gas molecules are initially confined within a sub-volume (V1) by a piston and the remaining volume V2 - Viis in vacuum. Let T., P., U1, S1, A1, H1, and G1 be the temperature, pressure, internal energy, entropy, Helmholtz free energy, enthalpy, and Gibbs free energy of the ideal gas at this state, respectively. Now, imagine that the piston is removed so that the gas has volume V2. After some time the system settles down to equilibrium again. Find T2, P2, U2, S2, A2, H2, and G2 all as f(P.V.T). Make a P-V plot and a T-S plot marking states 1 & 2.

Thermodynamics

Answer 1

Given, SotemInaulated antainer 7maulated antainer Piston Initfal volu me of gas Final volume of gas, v (ie after (V2-V .V. T. P.U.,S A,, M, G ve mavin Pioton) vaccum Initial condition ofa :phen gas expand againt J Vacaum the process is knouon FREE EXPANS IDN. as :In free expanaln process the work done io exo because the gas expando againast vacuum. 7.e FryiAter Removing Ploton Se APPlying Fieat la of Thermadyamis Syatem io inoulated, So and Sw in algo ero. du o Fos Ideal gas:mcdT 0

i.e. T,=T2 Notei- In free expanan of the ideal even initial and fal temperatures are Same , the Process in not Isotbermal because temperature chayes in between. vexy faot Procens (se, xepresented 6y dashad lne Final Tembera ture (T.)- T T Final Pressure we know, for Jdeal ga T2 P,V (TT) 11 P.V VI Finad Internl Energ7Previausly caleulated, duo we Tt Can abo be writen a

Find Entalty: we know + =1P i.e. H-H,- O Final Entrety: Fex Ideal gas, + T2-1Codn() Ti S,-SMNRM Fioal Helmhalts Free Enery A= CITS we A2 0r-TAZ u- T(NRIn) + S) = C-13) -NRT A.-NRT, M() A2

Finad Free Gilbbo Ener we kmew AG= 4H-T4s G0-7(ARn) T.= T, T2 T AS 4H O GG-NRTIn) T.-T2 P. p1 T1 V/L s VH Fij Pv dtagram of given Free expansim T-S Free exprmsion Notes Fxee expansim in very faot brocen and so can't be consdered Guasi-atatic procens. Hence it as iTreveraible proces theto why epreaeqted b Dashed Dne.