Q: An ideal gas mixture filled inside a balloon expands according to the relation $PV^{2/3} = constant $ . What will be the temperature inside the balloon
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Sol: $\large PV^{2/3} = constant $
⇒ $\large (\frac{nRT}{V}) V^{2/3} = constant $
$\large T V^{-1/3} = constant $
$\large V \propto T^3 $
Temperature increases with increase in volume.