A rigid cubical box of volume 1 cm3 filled with 1 mol of Helium at high pressure, is slowly cooled to 0 K, in your school laboratory. What will be the pressure on the bottom wall? Assume no interactions between the atoms other than elastic collisions
A rigid cubical box of volume 1 cm3 filled with 1 mol of Helium at high pressure, is slowly cooled to 0 K, in your school laboratory. What will be the pressure on the bottom wall? Assume no interactions between the atoms other than elastic collisions
The correct option is B 400 Pa
Well, this is all being done in your school laboratory which, presumably, is on Earth. The gravitational pull of Earth does not contribute to anything in the kinetic theory, since the kinetic energy of each particle far exceeds its gravitational potential energy. But as the kinetic energy approaches zero when you cool the gas towards 0K, it becomes more and more comparable to its gravitational potential energy; thus, the density of the gas starts increasing near the floor of the box as the molecules "fall”! If the box is left at 0K for a long enough time, it can be assumed that the gas will "settle” at the bottom, like a spoonful of salt.
Thus, no other wall of the box will experience any pressure, except the floor. The pressure on the floor will be purely due to the weight W of the gas.
∴P=Warea
=[(4×10−3kg)×10m/s210−4m2] Pa (∵ Molar mass of Helium=4 g; g=10m/s2)
= 400 Pa
Well, this is all being done in your school laboratory which, presumably, is on Earth. The gravitational pull of Earth does not contribute to anything in the kinetic theory, since the kinetic energy of each particle far exceeds its gravitational potential energy. But as the kinetic energy approaches zero when you cool the gas towards 0K, it becomes more and more comparable to its gravitational potential energy; thus, the density of the gas starts increasing near the floor of the box as the molecules "fall”! If the box is left at 0K for a long enough time, it can be assumed that the gas will "settle” at the bottom, like a spoonful of salt.
Thus, no other wall of the box will experience any pressure, except the floor. The pressure on the floor will be purely due to the weight W of the gas.
∴P=Warea
=[(4×10−3kg)×10m/s210−4m2] Pa (∵ Molar mass of Helium=4 g; g=10m/s2)
= 400 Pa
