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11.Thermodynamics
normal
Gas obey $P^2V =$ constant. The initial temperature and volume are $T_0$ and $V_0$. If gas expands to volume $2V_0$, its final temperature becomes
A
$\sqrt 2 {T_0}$
B
$2T_0$
C
$T_0/2$
D
${T_0}/\sqrt 2 $
Solution
$\mathrm{P}^{2} \mathrm{V}=\mathrm{constant}$
$\left(\frac{\mathrm{nRT}}{\mathrm{V}}\right)^{2} \mathrm{V}=\mathrm{constant} ; \frac{\mathrm{T}^{2}}{\mathrm{V}}=\mathrm{constant}$
$\frac{\mathrm{T}_{1}^{2}}{\mathrm{V}_{1}}=\frac{\mathrm{T}_{2}^{2}}{\mathrm{V}_{2}}$
$\frac{\mathrm{T}^{2}}{\mathrm{V}_{0}}=\frac{\mathrm{T}_{2}^{2}}{2 \mathrm{V}_{0}} \Rightarrow\left(\mathrm{T}_{2}=\sqrt{2} \mathrm{T}_{0}\right)$
Standard 11
Physics
