JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Heat & Thermodynamics

The average translational kinetic energy of a gas molecule is $\frac{3}{2}kT$, so it is fixed entirely by the temperature. Lowering the temperature therefore lowers this energy, so the first statement is correct. Raising the pressure at constant temperature leaves the temperature, and hence the average kinetic energy, unchanged, so the second statement is wrong, and for the same reason a change of volume alone does not alter it, so the third is wrong too. Read correctly as a constant-volume process, the fourth statement is Gay-Lussac's law, $P\propto T$, so the pressure does rise with temperature and the statement is correct. At constant pressure the volume grows with temperature by Charles's law rather than shrinking, so the fifth statement is wrong. Only the first and fourth statements hold.