An insulated high-pressure containment vessel used in laboratory experiments is shown below.
The internal chamber is a cube. Each side of this cube has length 0.40 m0.40\text{ m}0.40 m. The chamber is sealed and full of helium. Helium behaves as an ideal gas.
The vessel is initially at 17∘C17^\circ\text{C}17∘C. The helium in the chamber has an initial pressure of 150 kPa150\text{ kPa}150 kPa.
(i) Calculate the amount of helium nnn in the chamber in moles.
n=……………………………………………… moln = \dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\text{ mol}n=……………………………………………… mol
The temperature of the vessel is increased from 17∘C17^\circ\text{C}17∘C to 950∘C950^\circ\text{C}950∘C.
Calculate the pressure in kPa\text{kPa}kPa at 950∘C950^\circ\text{C}950∘C.
pressure=……………………………………………… kPa\text{pressure} = \dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\text{ kPa}pressure=……………………………………………… kPa
The temperature of the chamber is 950∘C950^\circ\text{C}950∘C. A single atom of helium is travelling horizontally towards the vertical side Y\mathbf{Y}Y of the chamber. The initial speed of this atom is 1500 m s−11500\text{ m s}^{-1}1500 m s−1. After collision, it rebounds at the same speed.
(i) Calculate the change in momentum Δp\Delta pΔp of this atom.
- mass of helium atom=6.6×10−27 kg\text{mass of helium atom} = 6.6 \times 10^{-27}\text{ kg}mass of helium atom=6.6×10−27 kg
Δp=……………………………………………… kg m s−1\Delta p = \dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\text{ kg m s}^{-1}Δp=……………………………………………… kg m s−1
Assume that this atom does not collide with any other helium atoms inside the chamber. Instead, it travels horizontally, making repeated collisions with the opposite vertical walls of the chamber.
1. Show that the atom makes about 1900 collisions with side Y\mathbf{Y}Y in a time interval of 1.0 s1.0\text{ s}1.0 s.
Calculate the average force FFF on side Y\mathbf{Y}Y made by the atom.
F=……………………………………………… NF = \dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\dots\text{ N}F=……………………………………………… N
Without calculation, explain how your answer to (b)(ii)2 could be used to estimate the total pressure exerted by the atoms of the helium gas in the chamber.