The root mean square velocity ($v_{rms}$) of a gas is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, where $T$ is the absolute temperature and $M$ is the molar mass. Given condition: $v_{rms}(H_2) = v_{rms}(O_2)$. Squaring both sides: $\frac{3RT_{H_2}}{M_{H_2}} = \frac{3RT_{O_2}}{M_{O_2}} \implies \frac{T_{H_2}}{M_{H_2}} = \frac{T_{O_2}}{M_{O_2}}$.

Data from sources:

1. Molar mass of Hydrogen ($H_2$): $2 \times 1.008 \approx 2 \text{ g/mol}$ .
2. Molar mass of Oxygen ($O_2$): $2 \times 16.00 = 32 \text{ g/mol}$ .
3. Temperature of Oxygen ($T_{O_2}$): $47^\circ\text{C}$. Converting to Kelvin: $T(K) = t(^\circ\text{C}) + 273.15$. $T_{O_2} = 47 + 273 = 320 \text{ K}$ .

Calculation: $\frac{T_{H_2}}{2} = \frac{320}{32}$ $\frac{T_{H_2}}{2} = 10$ $T_{H_2} = 20 \text{ K}$.