A) 9/11
B) 11/7
C) 12/7
D) 15/7
Correct Answer: B
Solution :
[b] :\[{{\gamma }_{mixture}}~=\frac{\frac{{{n}_{1}}{{\gamma }_{1}}}{{{\gamma }_{1}}-1}+\frac{{{n}_{2}}{{\gamma }_{2}}}{{{\gamma }_{2}}-1}}{\frac{{{n}_{1}}}{{{\gamma }_{1}}-1}+\frac{{{n}_{2}}}{{{\gamma }_{2}}-1}}~\] Here, \[{{n}_{1}}=3,{{\gamma }_{1}}=\frac{5}{3},{{n}_{2}}=1,{{\gamma }_{2}}=\frac{7}{5}\] \[{{\gamma }_{mixture}}=\frac{\frac{3\times \frac{5}{3}}{\left[ \frac{5}{3}-1 \right]}+\frac{1\times \frac{7}{5}}{\left[ \frac{7}{5}-1 \right]}}{\frac{3}{\left[ \frac{5}{3}-1 \right]}+\frac{1}{\left[ \frac{7}{5}-1 \right]}}\] \[=\frac{\frac{15}{2}+\frac{7}{2}}{\frac{9}{2}+\frac{5}{2}}=\frac{22}{14}=\frac{11}{7}\]
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