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Root Mean Square Speed

If for two ga...

Question

If for two gases of molecular weights $M_{A}$ and $M_{B}$ at temperature $T_{A}$ and $T_{B}$ , respectively, $T_{A} M_{B} = T_{B} M_{A}$ , then which property has the same magnitude for both the gases?

P V

if mass of gases taken are same

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Pressure

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KE per mole

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V_{r m s}

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Solution

The correct options are
A $P V$ if mass of gases taken are same
B $V_{r m s}$
When $\frac{T_{A}}{M_{A}} = \frac{T_{B}}{M_{B}}$ or $T_{A} M_{B} = T_{B} M_{A}$

$(P V)_{A} = n R T$ or $\frac{W_{A}}{M_{A}} R T_{A}$

$(P V)_{B} = \frac{W_{B}}{M_{B}} R T_{B}$

$∴ W h e n W_{A} = W_{B}$

$(P V)_{A} = (P V)_{B}$

$μ_{r m s} = \sqrt{\frac{3 R T}{M}}$

$∴ μ_{A} = \sqrt{\frac{3 R T_{A}}{M_{A}}}$

$μ_{B} = \sqrt{\frac{3 R T_{B}}{M_{B}}}$

$∴ μ_{A} = μ_{B}$ $∵ [\frac{T_{A}}{M_{A}} = \frac{T_{B}}{M_{B}}]$

Hence, the correct options are $A$ and $D$

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