A) \[\frac{5}{3}{{T}_{0}}\]
B) \[\frac{3}{2}{{T}_{0}}\]
C) \[\frac{4}{3}{{T}_{0}}\]
D) \[\frac{5}{4}{{T}_{0}}\]
Correct Answer: A
Solution :
Let T be the temperature of the mixture, then \[\operatorname{U}={{U}_{1}}+{{U}_{2}}\] \[\Rightarrow \,\,\,\frac{f}{2}({{n}_{1}}+{{n}_{2}})\,RT\] \[=\,\,\frac{f}{2}\left( {{n}_{1}} \right)\left( R \right)\left( {{T}_{0}} \right)\,\,+\,\,\frac{f}{2}\left( {{n}_{2}} \right)\left( R \right)\left( 2{{T}_{0}} \right)\] \[\Rightarrow \,\,\,\,(2+4)T=2{{T}_{0}}\,\,+\,\,8{{T}_{0}}\,\,\,\,(\because \,\,\,{{n}_{1}}=2,\,\,{{n}_{2}}=4)\] \[\therefore \,\,\,\,T=\frac{5}{3}\,{{T}_{0}}\]
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