Suppose ideal gas equation follows $V{P^3}$= constant. Initial temperature and volume of the gas are $T$ and $V$ respectively. If gas expand to $27V$ then its temperature will be come
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(b) $V{P^3}$= constant = $k$ ==> $P = \frac{k}{{{V^{1/3}}}}$
Also$PV = \mu RT$==>$\frac{k}{{{V^{1/3}}}}.V = \mu RT$==> ${V^{2/3}} = \frac{{\mu RT}}{k}$
Hence ${\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^{2/3}} = \frac{{{T_1}}}{{{T_2}}}$==> ${\left( {\frac{V}{{27V}}} \right)^{2/3}} = \frac{T}{{{T_2}}}$==> ${T_2} = 9\,T$
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