A) \[\operatorname{k}=\frac{1}{t}ln\left( \frac{{{P}_{\infty }}}{3\left( {{P}_{\infty }}-{{P}_{t}} \right)} \right)\]
B) \[\operatorname{k}=\frac{1}{t}ln\left( \frac{2{{P}_{\infty }}}{\left( {{P}_{\infty }}-{{P}_{t}} \right)} \right)\]
C) \[\operatorname{k}=\frac{1}{t}ln\left( \frac{3{{P}_{\infty }}}{2{{P}_{\infty }}-{{P}_{\operatorname{t}}}} \right)\]
D) \[\operatorname{k}=\frac{1}{t}ln\left( \frac{2{{P}_{\infty }}}{3\left( {{P}_{\infty }}-{{P}_{\operatorname{t}}} \right)} \right)\]
Correct Answer: D
Solution :
\[{{P}_{T}}={{P}_{0}}+2x\] |
\[x=\frac{{{P}_{T}}{{P}_{0}}}{2}\] |
\[k=\frac{1}{t}\ln \left( \frac{{{P}_{0}}}{{{P}_{0}}-x} \right)\] |
After long time, |
\[x=\frac{{{P}_{T}}-\frac{{{P}_{\infty }}}{3}}{2}\] |
\[k=\frac{1}{t}\ln \left( \frac{\frac{{{P}_{\infty }}}{3}}{\frac{{{P}_{\infty }}}{3}-\left( \frac{3{{P}_{T}}-{{P}_{\infty }}}{6} \right)} \right)\] |
\[{{P}_{\infty }}=3{{P}_{O}},x=\frac{3{{P}_{T}}-{{P}_{\infty }}}{6}\] |
\[k=\frac{1}{t}\ln \left( \frac{{{P}_{\infty }}/3}{\frac{{{P}_{\infty }}}{2}-\frac{{{P}_{T}}}{2}} \right)\] |
\[k=\frac{1}{t}\ln \left( \frac{2{{P}_{\infty }}}{3\left( {{P}_{\infty }}-{{P}_{T}} \right)} \right)\] |
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