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 :
The system of two rigid boxes is shown in figure. \[\underset{\text{a}\,\text{mole}\,{{\text{N}}_{\text{2}}}}{\mathop{}}\,\frac{{}}{\text{Thermal}\,\text{contact}}\underset{\text{a}\,\text{mole}\,\text{He}}{\mathop{}}\,\] We have,\[U=\frac{1}{2}nf({{T}_{f}}-{{T}_{i}})\] \[\Delta {{U}_{A}}=1\times \frac{5R}{2}({{T}_{f}}-{{T}_{0}})\] \[\Delta {{U}_{B}}=1\times \frac{3R}{2}\left( {{T}_{f}}-\frac{7}{3}{{T}_{0}} \right)\] Now,\[\Delta {{U}_{A}}+\Delta {{U}_{B}}=0\] \[\frac{5R}{2}({{T}_{f}}-{{T}_{0}})+\frac{3R}{2}\left( {{T}_{f}}-\frac{7{{T}_{0}}}{3} \right)=0\] \[5{{T}_{f}}-5{{T}_{0}}+3{{T}_{f}}-7\,{{T}_{0}}=0\] \[\Rightarrow \]\[8{{T}_{f}}=12{{T}_{0}}\]\[\Rightarrow \]\[{{T}_{f}}=\frac{12}{8}{{T}_{0}}=\frac{3}{2}{{T}_{0}}\]You need to login to perform this action.
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