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Q.

If the root mean square speed of hydrogen molecules is equal to root mean square speed of oxygen molecules at $47 ° C$ , the temperature of hydrogen is-

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a

$20 K$

b

$80 K$

c

$47 K$

d

$50 K$

answer is A.

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Detailed Solution

$For oxygen V_{O_{2}} = \sqrt{\frac{3 R T_{O_{2}}}{M_{O_{2}}}} v_{H_{2}} = \sqrt{3 R \frac{T_{H_{2}}}{M_{H_{2}}}} According to problem = \sqrt{\frac{3 R T_{O_{2}}}{M_{O_{2}}}} = \sqrt{3 R \frac{T_{H_{2}}}{M_{H_{2}}}} \frac{T_{O_{2}}}{M_{O_{2}}} = \frac{T_{H_{2}}}{M_{H_{2}}} \Rightarrow \frac{T_{H_{2}}}{(273 + 47)} = \frac{2}{32} T_{H_{2}} = 20 K$

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