A) \[\frac{\sqrt{3}+1}{\sqrt{3}-1}\]
B) \[\frac{\sqrt{3}-1}{\sqrt{3}+1}\]
C) \[\sqrt{3}:1\]
D) \[1:\sqrt{3}\]
Correct Answer: A
Solution :
\[\operatorname{Given} relation P{{V}^{{}^{3}/{}_{2}}} = constant\] \[\operatorname{Adiabatic} equation P{{V}^{\gamma }} = constant\] \[\operatorname{On} comparing we get \gamma = \frac{3}{2}\] \[{{\operatorname{V}}_{1}}={{V}_{o}}{{\operatorname{V}}_{2}}=\frac{{{V}_{o}}}{2}\] Apply equation for adiabatic process relate V \[{{\operatorname{T}}_{1}}{{\operatorname{V}}_{1}}^{\gamma -1}={{\operatorname{T}}_{2}}{{\operatorname{V}}_{2}}^{\gamma -1}_{used in Adiabtic}^{Important equation}\] \[{{\operatorname{T}}_{1}}{{\left( {{\operatorname{V}}_{\operatorname{o}}} \right)}^{\gamma -1}}={{\operatorname{T}}_{2}}{{\left[ \frac{{{\operatorname{V}}_{\operatorname{o}}}}{2} \right]}^{\gamma -1}}\] \[_{P{{V}^{\gamma }}=K}^{process}\] \[{{\operatorname{T}}_{2}}=T{{\left( 2 \right)}^{\gamma -1}}\] \[_{{{\operatorname{P}}^{1-\gamma }}{{T}^{\gamma }}=K}^{T{{V}^{\gamma -1}}=K}\] \[{{\operatorname{T}}_{2}}=T{{\left( 2 \right)}^{{}^{3}/{}_{2}-1}}\] \[{{\operatorname{T}}_{2}}=\sqrt{2}T\]
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