A) \[\frac{25}{8}\frac{{{P}_{0}}{{V}_{0}}}{R}\]
B) \[\frac{25}{4}\frac{{{P}_{0}}{{V}_{0}}}{R}\]
C) \[\frac{25}{16}\frac{{{P}_{0}}{{V}_{0}}}{R}\]
D) \[\frac{5}{8}\frac{{{P}_{0}}{{V}_{0}}}{R}\]
Correct Answer: A
Solution :
Temperature at A = \[\frac{3{{P}_{0}}V}{nR}\] Temperature at\[b=\frac{{{P}_{0}}\times 2{{V}_{0}}}{nR}\] Maximum temperature can be between B and C P-V equation for process BC \[P-3{{P}_{0}}=\frac{{{P}_{0}}-3{{P}_{0}}}{2{{V}_{0}}-{{V}_{0}}}\times (V-{{V}_{0}})\] \[P-3{{P}_{0}}=\frac{-2{{P}_{0}}V}{{{V}_{0}}}+2{{P}_{0}}\] \[P=\frac{-2{{P}_{0}}V}{{{V}_{0}}}+2{{P}_{0}}\] Multiply by V \[PV=\frac{-2{{P}_{0}}V}{{{V}_{0}}}+5{{P}_{0}}\] \[RT=-\frac{2{{P}_{0}}}{{{V}_{0}}}{{V}^{2}}+5{{P}_{0}}V\] Make \[\frac{dT}{dV}=0\] This gives \[T=\frac{25{{P}_{0}}{{V}_{0}}}{8R}\]You need to login to perform this action.
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