During an experiment an ideal gas is found to obey an additional law $\mathrm{V}^{2} \mathrm{P}=$ co

Question

During an experiment an ideal gas is found to obey an additional law $\mathrm{V}^{2} \mathrm{P}=$ constant. The\ gas is initially at temperature T and volume V . When it expands to a volume 2 V , the temperature becomes\

Professor PC Thomas Classes · Answer

$\mathrm{V}^{2} \mathrm{P}=$ constant (given) But $\mathrm{PV}=\mathrm{RT}$ for 1 mole $$\begin{equation*} \frac{(1)}{(2)}=\frac{\mathrm{V}^{2} \mathrm{P}}{\mathrm{PV}}=\frac{	ext { const }}{\mathrm{RT}} 	ag{2} \end{equation*}$$ $	herefore \mathrm{VT}=\mathrm{const}$\ $\mathrm{VT}=\mathrm{V}^{\prime} \mathrm{T}^{\prime}$\ $\mathrm{VT}=(2 \mathrm{~V}) \mathrm{T}^{\prime}$\ $	herefore \mathrm{T}^{\prime}=\frac{\mathrm{T}}{2}$\