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Thermal physics (A-level only)

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Question 18

An experimental cryogenic calibration chamber of volume V V\,V contains a gaseous mixture of helium-4 (He\text{He}He) and xenon-136 (Xe\text{Xe}Xe) atoms. The mixture is maintained in thermal equilibrium at a temperature of 180 K.

a.

State the relationship between the mean kinetic energies of the helium-4 atoms and the xenon-136 atoms in this mixture.

[1]
b.

Calculate the root mean square speed (crmsc_{\text{rms}}crms​) of the helium-4 atoms at this temperature.

  • Molar mass of helium-4 = 4.00 × 10-3 kg mol-1
  • Universal gas constant R=8.31 J mol−1 K−1R = 8.31\text{ J mol}^{-1}\text{ K}^{-1}R=8.31 J mol−1 K−1
  • Avogadro constant NA=6.02×1023 mol−1N_{\text{A}} = 6.02 \times 10^{23}\text{ mol}^{-1}NA​=6.02×1023 mol−1
  • Boltzmann constant kB=1.38×10−23 J K−1k_{\text{B}} = 1.38 \times 10^{-23}\text{ J K}^{-1}kB​=1.38×10−23 J K−1
[3]
c.

Explain, in terms of the kinetic theory model, how reducing the temperature of the gas mixture decreases the pressure it exerts on the inner walls of the chamber.

[4]

Thermal physics (A-level only) Questions

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