At what temperature would the rms speed of chlorine-35 atoms equal the following speeds? (Note: The mass of a chlorine-35 atom is 5.81 ✕ 10−26 kg.)
(a) the escape speed from Earth, 1.12 ✕ 104 m/s
(b) the escape speed from the Moon, 2.37 ✕ 103 m/s
From the kinetic theory Kinetic energy of particles
(½mv²) = (3/2) kT
mv² = 3kT
T = mv² / 3k ----------(1)
where v = escape velocity
m = mass of atom = 5.81 ? 10-26 kg
k = Boltzmann constant 1.38-23 J/(K.particle)
a)
from equation 1
T = mv² / 3k = 5.81 ? 10-26*[1.12 ? 104]2 / 3*1.38*10-23
T = 1.760*105 K
(b)
T = mv² / 3k = 5.81 ? 10-26*[2.37 ? 103]2 / 3*1.38*10-23
T = 7.88*103 K
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