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Thermal Properties Of Matter

Question

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere?
(Given: Mass of oxygen molecule (m) = 2.76 x 10^-26 kg
Boltzmann's constant k_B = 1.38 x 10^-23 JK^-1)

2.508 × 10⁴ K

8.360 × 10⁴ K

1.254 × 10⁴ K

5.016 × 10⁴ K

Solution

8.360 × 10⁴ K

Let at temperature T rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere

V_escape = 11200 m/s

Also, V_rms = V_escape = $\sqrt{\frac{3 k_{B} T}{m_{O_{2}}}} = 11200 m / s$

Putting value of K_B and m_O2 we get,

T = 8.360 x 10⁴ K