The r.m.s speed of oxygen molecules at 47°C is equal to that of the hydrogen molecules kept a $t______°C.$ (Mass of oxygen molecule/mass of hydrogen molecule=32/2)
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The r.m.s speed of oxygen molecules at 47°C is equal to that of the hydrogen molecules kept a t______°C. (Mass of oxygen molecule/mass of hydrogen molecule=32/2)

G1 Physics · Accepted Answer

For an ideal gas, vᵣₘₛ = √(3RT/M). Equal rms speeds imply T(O₂)/M(O₂) = T(H₂)/M(H₂). For oxygen, T(O₂) = 47 + 273 = 320 K. Given, M(O₂)/M(H₂) = 32/2. Therefore, 320/32 = T(H₂)/2. Hence, T(H₂) = 20 K. Convert to Celsius: T(H₂) = 20 - 273 = -253°C. Correct option: C.