A) \[\frac{(\gamma -1)}{2(\gamma +1)R}M{{v}^{2}}K\]
B) \[\frac{(\gamma -1)}{2\gamma }M{{v}^{2}}K\]
C) \[\frac{\gamma M{{v}^{2}}}{2R}K\]
D) \[\frac{(\gamma -1)}{2R}M{{v}^{2}}K\]
Correct Answer: D
Solution :
| [d] \[\frac{1}{2}\,M{{v}^{2}}=1\cdot {{C}_{V}}\Delta T\] |
| \[\Rightarrow \] \[\frac{1}{2}M{{v}^{2}}=\frac{R}{\gamma -1}.\Delta T\] |
| \[\Rightarrow \] \[\Delta T=\frac{M{{v}^{2}}(\gamma -1)}{2R}=\frac{(\gamma -1)M{{v}^{2}}}{2R}\] |
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