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We use the formula v^2 = 3RT/M for calculating the rms speed in both questions:
(a) v^2 = 3RT/M, where v is the escape speed from Earth
(1.12 x 104)2 = (3 x 8.314 x T)/(44.01)
T = 2.21 x 108
(b) v^2 = 3RT/M, where v is the escape speed from the Moon
(2.37 x 103)2 = (3 x 8.314 x T)/(44.01)
T = 9.91 x 106 Kelvins
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