A) \[{{U}_{m}}(T)={{U}_{m}}(0)+3RT\][Linear molecule, translation only]
B) \[{{U}_{m}}(T)={{U}_{m}}(0)+\frac{5}{2}RT\][Linear molecule translation and rotation only]
C) \[{{U}_{m}}(T)={{U}_{m}}(0)+\frac{3}{2}RT\][Non-linear molecule, translation and rotation only]
D) \[{{U}_{m}}(T)={{U}_{m}}(0)+RT\] [Non-linear molecule, translation only]
Correct Answer: B
Solution :
\[\Delta {{U}_{m}}={{C}_{V}}\Delta T\] \[{{\Delta }_{m}}(T)-{{U}_{m}}(0)={{C}_{V}}(T-0)\] \[{{U}_{m}}(T)-{{U}_{m}}(0)=\frac{5}{2}RT\] [\[Cv=\frac{5}{2}R,\] for linear molecule, by taking translational and rotational]\[{{U}_{m}}(T)={{U}_{m}}(0)+\frac{5}{2}RT\]
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