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 :
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.
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