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Standard XII

Physics

Temperature

The mass of m...

Question

The mass of molecule $A$ is twice that of molecule $B$ . The root mean square velocity of molecule $A$ is twice that of molecule $B$ . If two containers of equal volume have same number of molecules, the ratio of pressure $\frac{P_{A}}{P_{B}}$ will be

8 : 1

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1 : 8

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4 : 1

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1 : 4

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Solution

The correct option is A $8 : 1$
$W_{A} = 2 W_{B}$
$V_{A} = V_{B}$
Hence, $d_{A} = 2 d_{B}$
$u = \sqrt{\frac{3 P}{d}}$
$\frac{u_{A}}{u_{B}} = \sqrt{\frac{P_{A}}{P_{B}}} \times \sqrt{\frac{d_{B}}{d_{A}}}$
$2 = \sqrt{\frac{P_{A}}{P_{B}} \times \frac{1}{2}}$
$\frac{P_{A}}{P_{B}} = 8 : 1$

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The mass of molecule A is twice that of molecule B. The root mean square velocity of molecule A is twice that of molecule B. If two containers of equal volume have same number of molecules, the ratio of pressure PAPB will be

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The mass of molecule $A$ is twice that of molecule $B$ . The root mean square velocity of molecule $A$ is twice that of molecule $B$ . If two containers of equal volume have same number of molecules, the ratio of pressure $\frac{P_{A}}{P_{B}}$ will be

The correct option is A $8 : 1$
$W_{A} = 2 W_{B}$
$V_{A} = V_{B}$
Hence, $d_{A} = 2 d_{B}$
$u = \sqrt{\frac{3 P}{d}}$
$\frac{u_{A}}{u_{B}} = \sqrt{\frac{P_{A}}{P_{B}}} \times \sqrt{\frac{d_{B}}{d_{A}}}$
$2 = \sqrt{\frac{P_{A}}{P_{B}} \times \frac{1}{2}}$
$\frac{P_{A}}{P_{B}} = 8 : 1$