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Homework Statement
-We have a cylinder with two chambers separated by an adiabatic piston. The external walls are adiabatics but left wall is diatermana. Friction produced by the piston moving is absorbed by the right system. Inicially gas conditions are the same for both ( in the left chamber CO2, 500 litres, 1 Bar, 27 ºC, and in right chamber N2 with the same conditions).
We add heat (by an exterior focus with constant temperature of 900ºK) through diatemana wall and piston moving until pressure in right chamber is 2 Bar. Left system is a polytropic process with n = -2. We assume gases are perfect.
Calculate:
a) P,T,V in final equilibrium in both chambers
b) ΔU , heat and work in left chamber
c) ΔU , heat and work in right chamber
d) Expansion work and friction work in right chamber
Homework Equations
The Attempt at a Solution
a) First I find moles for both gases and It`s the same 20.32 moles.
Final pressure in both chambers is 2 Bar. To calculate final temperature in left chamber I used [tex]T_2=T_1(P_2/P_1)^{n-1/n} [/tex]and it is [tex] T_2=848,52 ºK.[/tex]
For the volume [tex] P_1(V_1)^n=P_2(V_2)^n [/tex] and it is [tex]V_2= 707,1 Litres[/tex]
For the right chamber: Total volume of the cylinder is 1000 litres and doesn´t change, so [tex]V_t=V_{1f}-V_{2f}, 1000=707,1-V_{2f}, V_{2f}=292,9 litres[/tex] now I used [tex]PV=NRT[/tex] to calculate final temperature in right chamber [tex]T=351,57 ºK.[/tex]
b) To calculate ΔU, I use [tex]ΔU= N Cv(Tf-Ti)[/tex] and [tex] ΔU=229.0788 Kj [/tex] after
[tex]W_{exp}=NR(T_f-T_i)/1-n [/tex] and [tex]W_{exp}=30.8901 Kj [/tex] Now I calculate Q
[tex] Q= ΔU+W_{exp}=198.1887 Kj [/tex]
I don´t know if it´s ok?
Thank you