Respuesta :
The temperature of the hydrogen gas molecules is 81818.9127×10²³K if it has Root mean square speed of 410m/sec.
Root mean square speed (v[tex]_r_m_s[/tex]) is characterized as the square foundation of the mean of the square of velocities, everything being equal. It is indicated by v[tex]_r_m_s[/tex] = √v₂
(I) RMS speed is straightforwardly relative to square base of the temperature and conversely corresponding to square foundation of mass of the particle. At a provided temperature with the particles of lighter mass move quicker on a normal than the atoms with heavier masses.
Lighter particles like hydrogen and helium have high 'v[tex]_r_m_s[/tex]' than heavier particles like oxygen and nitrogen at a similar temperature.
(ii) Expanding the temperature will speed up particles
We know that RMS speed of the gas molecules is given by the below formula
v=√(3kT)/m
where k is Boltzmann constant
T is the temperature of gas molecules
and m is the mass of gas molecules
So, putting value of k=1.380649×10⁻²³ J⋅K⁻¹,m=2.016g,v=410m/sec, T=?
=>410=√(3×1.380649×10⁻²³ ×T)/2.1016
Squaring on both sides, we get
=>(3×1.380649×10⁻²³ ×T)/2.1016=410×410
=>T=(410×410×2.1016) / (3×1.380649×10⁻²³)
=>T=(338889.6 / 4.141947) × 10⁻²³
=>T=81818.9127×10²³K
Hence, required temperature is 81818.9127×10²³K.
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(Complete question) is:
Hydrogen molecules; with molar mass of 2.016 g mol certain gas have an rms speed of 410 m s What is the temperature of this gas in kelvins?
