Thank you for the opportunity to help you with your question!

This Question is currently still in progress and will be
finished shortly

Please find the solution enclosed here with .. In case of any doubt please feel free to ask… Do not forget to best my answer… If you are having some other problem please feel free to contact me for quick & quality services..

Jun 21st, 2015

According to Kinetic theory of gases we know that

Kinetic energy (½mv²) = (3/2) kT

or ; mv² = 3kT
T = mv² / 3k .. ..

v = escape velocity , k = Boltzmann constant 1.38^-23 J/(K.particle) &

T = temperature K

(a) the escape speed from Earth, 1.12 ✕ 10^{4} m/s
T = 3.32* 10^-26 kg x (1.12 *10^4 m/s)² / (3 x 1.38*10^-23) .. .. T = 1.0 x 10 ^5 K

(b) the escape speed from the Moon, 2.37 ✕ 10^{3} m/s
T = 3.32* 10^-26 kg x (2.37 *10^3 m/s)² / (3 x 1.38*10^-23) .. .. T = 4.5 x 10 ^3 K