5. Entropy of Reversible Mixing of Ideal Gases. What is the...

5. Entropy of Reversible Mixing of Ideal Gases. What is the change in entropy, ?mixS, associated with mixing two ideal gases of different kinds (? and ?) reversibly? This can be accomplished in a special container with two semi-permeable pistons that each only allow only one type of gas to pass through, as shown, that can be slowly moved apart. The number of ? molecules is N? and the number of ? molecules is N?. The volumes of their initial containers are V1 and V2, and P1 = P2 = Pf, as shown. Solve using classical thermodynamics, not statistical thermodynamics in this case. Initial State V1, P1 V2, P2 Final State Vf = V1 + V2, Pf piston permeable only to ? piston permeable only to ? **Hint: compare the work done by each gas on the opposite respective piston as the pistons are moved apart (and recall the thermodynamic definition of entropy). Each gas can only perform reversible PV-type work on the piston which it cannot diffuse through. The temperature of the container is held constant, so the change in internal energy is also constant throughout this process (these are ideal gases).

Transcript

00:01 Hello student we have one question that is asked here we find the value of a del s mix that means you write the formula of del s mix so now here we have given the thermodynamics case so here we have given what a semi permable piston so here we draw for the structure for it here we are drawing but the semi permable piston so here the press v1 b1 so we here it is connected with so the another one here drawing for it here drawing what are here drawing for it so here it is the one then here will draw for it so here we drawing what for it so it is in this position v2 p2 is present so it is our what semi permable here writer semi permable here is a certain so now here after removal we write it which is gives us to what after removal so it will give the product so here you draw the structure of the product so it will give what this type of product so here you draw what the product structure so here we are drawing what the product structure so here we here we are drawing what the product structure here we are doing what the product structure so this is the product which is you write it vf is equal to v1 plus v2 so here write out pf so now here let we know the two ideal gas with the initial parameter which is you write word n1 b1 then you write out n1 b1 then you write word p1 so now here you write and n2 then you write 2 b2 then here write 2 p 2 so now these are what the gas which is mixed in the adiabatic contamination here write what these are you write what these are what gases these are gases are mixed you write what are mixed in an adiabatic you write word a adabatic container here is adabatic container so a diabatic container that means as we set the course in that means each each of the allow only one type of gases to passes through it so we know the change in entropy here which is right but the change in entropy so which is ds which is equal to integration from dq divided by t so now we can write it imply that a d s is equal to integration from du plus p dv divided by t so we know d u is equal to but you're right they d u is equal to ncv d t so here the p is equal to what n r t divided by v so here we putting this value so now we can write it imply that d s is equal to integration from t i to t f so here which is right what nc v which is right ncv which is right ncb d t divided by by t plus you write where the integration from here write the integration from what v i to b f so which is here written n r dv divided by v so now we can write but we know that the pv is equal to you write to pv is equal to n r t so now in the what v is the what here you're taking the v so now we can write pf divided by p i which is equal to tf divided…

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