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 0.35 m0.35\text{ m}0.35 m. The chamber is sealed and full of argon. Argon behaves as an ideal gas.
The vessel is initially at 27∘C27^\circ\text{C}27∘C. The argon in the chamber has an initial pressure of 240 kPa240\text{ kPa}240 kPa.
Calculate the amount of argon 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 27∘C27^\circ\text{C}27∘C to 850∘C850^\circ\text{C}850∘C.
Calculate the pressure in kPakPakPa at 850∘C850^\circ\text{C}850∘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 850∘C850^\circ\text{C}850∘C. A single atom of argon is travelling horizontally towards the vertical side Y\mathbf{Y}Y of the chamber. The initial speed of this atom is 750 m s−1750\text{ m s}^{-1}750 m s−1. After collision, it rebounds at the same speed.
Calculate the change in momentum Δp\Delta pΔp of this atom.
- mass of argon atom=6.6×10−26 kg\text{mass of argon atom} = 6.6 \times 10^{-26}\text{ kg}mass of argon atom=6.6×10−26 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 argon atoms inside the chamber. Instead, it travels horizontally, making repeated collisions with the opposite vertical walls of the chamber.
Show that the atom makes about 1100 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 argon gas in the chamber.