A) \[{{p}_{A}}+{{x}_{A}}({{p}_{B}}-{{p}_{A}})\]
B) \[{{p}_{A}}+{{x}_{A}}({{p}_{A}}-{{p}_{B}})\]
C) \[{{p}_{B}}+{{x}_{A}}({{p}_{B}}-{{p}_{A}})\]
D) \[{{p}_{B}}+{{x}_{A}}({{p}_{A}}-{{p}_{B}})\]
Correct Answer: D
Solution :
[d] Total pressure,\[{{p}_{T}}=p{{'}_{A}}+p{{'}_{B}}\] ...(i) |
We know that, \[p{{'}_{A}}={{p}_{A}}{{x}_{A}}\] |
\[p{{'}_{B}}={{p}_{B}}{{x}_{B}}\] |
Substituting the values of \[p{{'}_{A}}\]and \[p{{'}_{B}}\] in Eq. (i) |
\[{{p}_{T}}={{p}_{A}}{{x}_{A}}+{{p}_{B}}{{x}_{B}}\] |
\[[{{x}_{A}}+{{x}_{B}}=1\Rightarrow {{x}_{A}}=1-{{x}_{B}}or\,{{x}_{B}}=1-{{x}_{A}}]\] |
\[={{p}_{A}}{{x}_{A}}+{{p}_{B}}(1-{{x}_{A}})\] |
\[={{p}_{A}}{{x}_{A}}+{{p}_{B}}-{{p}_{B}}{{x}_{A}}\] |
\[\therefore \] \[{{p}_{T}}x{{p}_{B}}+{{x}_{A}}({{p}_{A}}-{{p}_{B}})\] |
You need to login to perform this action.
You will be redirected in
3 sec