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(A) The average kinetic energy of an ideal gas molecule is given by the formula $KE_{	ext{avg}} = \frac{3}{2} k_B T$,where $k_B$ is the Boltzmann con

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$(1)$ and $(4)$ only

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(A) The average kinetic energy of an ideal gas molecule is given by the formula $KE_{	ext{avg}} = \frac{3}{2} k_B T$,where $k_B$ is the Boltzmann constant and $T$ is the absolute temperature.Statement $(1)$ is correct: Since $KE_{	ext{avg}} \propto T$,decreasing the temperature decreases the average kinetic energy.Statement $(2)$ is incorrect: At constant temperature,$KE_{	ext{avg}}$ remains constant regardless of pressure changes.Statement $(3)$ is incorrect: At constant temperature,$KE_{	ext{avg}}$ remains constant regardless of volume changes.Statement $(4)$ is correct: According to Gay-Lussac's Law,at constant volume,the pressure of a gas is directly proportional to its absolute temperature $(P \propto T)$.Statement $(5)$ is incorrect: According to Charles's Law,at constant pressure,volume is directly proportional to temperature $(V \propto T)$,so volume increases with temperature.Therefore,statements $(1)$ and $(4)$ are correct.

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