A) \[{{T}_{f}}=\frac{3}{7}{{T}_{0}}\]
B) \[{{T}_{f}}=\frac{7}{3}{{T}_{0}}\]
C) \[{{T}_{f}}=\frac{3}{2}{{T}_{0}}\]
D) \[{{T}_{f}}=\frac{5}{2}{{T}_{0}}\]
Correct Answer: C
Solution :
Here, change in internal energy of the system is zero. i.e., increase in internal energy of one is equal to decrease in internal energy of other. \[\Delta {{U}_{A}}=1\times \frac{5R}{2}({{T}_{f}}-{{T}_{0}})\] \[\Delta {{U}_{B}}=1\times \frac{3R}{2}\left( {{T}_{f}}-\frac{7}{3}{{T}_{0}} \right)\] Now, \[\Delta {{U}_{A}}+\Delta {{U}_{B}}=0\] \[\Rightarrow \]\[\frac{5R}{2}({{T}_{f}}-{{T}_{0}})+\frac{3R}{2}\left( {{T}_{f}}-\frac{7{{T}_{0}}}{3} \right)=0\] \[\Rightarrow \]\[5{{T}_{f}}-5{{T}_{0}}+3{{T}_{f}}-7{{T}_{0}}=0\] \[\Rightarrow \]\[8{{T}_{f}}=12{{T}_{0}}\] \[\Rightarrow \]\[{{T}_{f}}=\frac{2}{8}{{T}_{0}}=\frac{3}{2}{{T}_{0}}\]You need to login to perform this action.
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