Question

An ideal gas mixture filled inside a balloon expands according to relation PV^2/3=constant. The temperature inside the balloon is
A)increasing B)decreasing C)constant D)can't be said

Answer 1

Dear Student,

$$\begin{gathered} {\mathrm{PV}}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=\mathrm{constant} \\ \mathrm{We}\mathrm{know}\mathrm{that} \\ \mathrm{PV}=\mathrm{RT} \\ \mathrm{P}=\frac{\mathrm{RT}}{\mathrm{V}} \\ \left(\frac{\mathrm{RT}}{\mathrm{V}}\right){\mathrm{V}}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=\mathrm{constant} \\ {\mathrm{RTV}}^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=\mathrm{constant} \\ \mathrm{T}\mathrm{\alpha }{\mathrm{V}}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} \\ \mathrm{with}\mathrm{increase}\mathrm{in}\mathrm{the}\mathrm{volume}\mathrm{the}\mathrm{temperature}\mathrm{is}\mathrm{also}\mathrm{increases} \end{gathered}$$