question_answer

A gas expands in such a manner that its pressure and volume comply with the condition \[\mathbf{P}{{\mathbf{V}}^{\mathbf{2}}}\mathbf{=}\]constant. Will the gas cool or get heated on expansion?

Answer:

                For a perfect gas, \[\frac{PV}{T}=\]constant \[(K)\] Given \[\text{P}{{\text{V}}^{\text{2}}}=\]constant \[\left( K' \right)\] \[\therefore \]  \[P=\frac{K'}{{{V}^{2}}}\] \[\therefore \]  \[\frac{K'}{{{V}^{2}}}.\frac{V}{T}=K\]   or \[VT=\frac{K'}{K}=\]constant Hence   \[V\propto \frac{1}{T}\] That is the expansion of the gas will result in the decrease of temperature.