Question

The escape velocity from the Moon is much smaller than that from the Earth, only 2.38 km/s. At what temperature would hydrogen molecules (molar mass is equal to 2.016 g/mol) have a root-mean-square velocity vrms equal to the Moon’s escape velocity?

Answer 1

Answer:

457.8394 K

Explanation:

$v_e$ = Escape velocity = 2.38 km/s

T = Temperature

R = Gas constant = 8.314 J/mol K

M = Molar mass = 2.016 g/mol

The rms velocity of a molecule is given by

$v_r=\sqrt{\frac{3RT}{M}}\\\Rightarrow v_r^2=\frac{3RT}{M}\\\Rightarrow T=\frac{v_r^2M}{3R}$

Here, $v_r=v_e=2.38\ km/s$

$T=\frac{v_e^2M}{3R}\\\Rightarrow T=\frac{(2.38\times 10^3)^2\times 2.016\times 10^{-3}}{3\times 8.314}\\\Rightarrow T=457.8394\ K$

The temperature of the hydrogen molecule would be 457.8394 K