Question

B. Two distinguishable monatomic ideal gases A and B are held in a volume V by a movable partition of zero weight and volume. The relative proportions of A and B are arbitrary as the system is in equilibrium (i.e., the pressure P and temperature T are uniform throughout the system). Let N = N , +N be the total number of molecules and let x be the fraction of speed or (NB = XN). (a) Calculate the change in entropy of the system (in terms of N and x) when the partition is removed. (b) How much heat Q and W are applied to the system? (c) Is Q =TAS ? State why to support your answer?

Answer 1

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Colution Ca.) ONCEPT: Change in entropy when AYAtem goei from Volume A to Volume e givan by VA Boltanann oomtant here NA J number and k it ofmoleculen Here change in entropy A -0) A Bince VA=4 tv; PV: NAKThere Pand T tanta are ConA uing and NANB ()N+XN C1-x)N NA A - (i V,4 V 1-x Y;A and V+6 NI fvom e (ii and (i) houw 1 5NK (1-x)Jn 1- NA- (1-3N and NN since

ii) AS--NK b Since during the whole proce8s T- Conatant and at conatant T hence fro du- dq-w Je have W - Pdv fror PV- NKT P NKT A NAKT dVNKi V dv Ng KTIn V Vi A NA KT Jn V again from e(ii)Cii) and using giver NA NCx) and Ne= Nx W= -NKT hence theat applied w = NKT (c) Clearly rom eahin)and (iv) Q= TAS Since du o hence all he energy gven uged to Yaise he entnopy hence a- TAS
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