The Crystallization Chamber · AI Generator #GEN-96BE1AC8

Physics · thermodynamics

Problem

A materials scientist is developing a novel crystallization process in a sealed chamber. The chamber initially contains

N = 10^{20}

gas molecules at temperature

T_0 = 400\;\text{K}

and pressure

p_0 = 2.0\;\text{atm}

. The crystallization process works by selectively removing only those molecules whose speeds exceed a threshold value

v_\text{thresh} = 800\;\text{m/s}

from the gas phase (they condense onto crystal surfaces). After this selective removal process reaches equilibrium, the remaining gas molecules redistribute their velocities according to the Maxwell-Boltzmann distribution at a new temperature

T_f

. The scientist observes that exactly

25\%

of the original molecules remain in the gas phase. (a) What is the final temperature

T_f

of the remaining gas? (b) What is the final pressure in the chamber, assuming the volume remains constant? Take the molecular mass to be

m = 3.0 \times 10^{-26}\;\text{kg}

and

k_B = 1.38 \times 10^{-23}\;\text{J/K}

Related theory

thermodynamics

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