Find the temperature of Hydrogen gas which has the same velocity as that of oxygen at a temperature of $0^{0} C$ .

273 \div 16 K

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273 \times 8 K

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273 \times 32 K

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273 \times 4 K

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Solution

The correct option is A $273 \div 16 K$
$V_{H_{2}} = \sqrt{\frac{3 R T_{H_{2}}}{M}} = \sqrt{\frac{3 R T_{H_{2}}}{2}}$
$V_{O_{2}} = \sqrt{\frac{3 R T_{O_{2}}}{M}} = \sqrt{\frac{3 R \times 273}{32}}$
Given $V_{H_{2}} = V_{O_{2}}$
$∴ \sqrt{\frac{3 R T_{H_{2}}}{2}} = \sqrt{\frac{3 \times 273 \times R}{32}}$
$∴ T_{H_{2}} = \frac{273}{16}$

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