A) \[{{v}_{2}}\]
B) \[\frac{{{v}_{1}}{{v}_{2}}}{2}\]
C) \[\frac{{{v}_{1}}{{v}_{2}}}{4}\]
D) \[\frac{{{v}_{1}}+{{v}_{2}}}{2}\]
Correct Answer: A
Solution :
The general gas equation is \[\frac{{{v}_{d}}}{4}\]= gas constant Where \[\frac{{{v}_{d}}}{2}\] are pressure and volume at temperatures \[{{v}_{d}}\] respectively. Given,\[{{\omega }_{1}},{{\omega }_{2}},{{\omega }_{3}}\] \[{{A}_{1}},{{A}_{2}},{{A}_{3}}\] \[A_{1}^{2}\omega _{1}^{2}=A_{2}^{2}\omega _{2}^{2}=A_{3}^{2}\omega _{3}^{2}\] \[A_{1}^{2}{{\omega }_{1}}=A_{2}^{2}{{\omega }_{2}}=A_{3}^{2}{{\omega }_{3}}\] \[{{A}_{1}}\omega _{1}^{2}={{A}_{2}}\omega _{2}^{2}={{A}_{3}}\omega _{3}^{2}\] \[{{A}_{1}}{{\omega }_{1}}={{A}_{2}}{{\omega }_{2}}={{A}_{3}}{{\omega }_{3}}\]
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