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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Chemistry
Chapter: States of Matter

NTA Abhyas 2020 · Chemistry · States of Matter

What will be the relation between the T _ 1 of gas 1 with M _ 1 =...

What will be the relation between the

{T}_{1}

of gas 1 with

{M}_{1} = 56

and

{T}_{2}

of gas 2 with

{M}_{2} = 44

if the average speed of gas 1 is equal to most probable speed of gas 2?

Options

A ${T}_{1} = {T}_{2}^{2}$
B ${T}_{1} = {T}_{2}$
C ${T}_{1} = ( {T}_{2}{)}^{\dfrac{1}{2}}$
D ${T}_{1} = \dfrac{1}{{T}_{2}}$

Correct answer

B. ${T}_{1} = {T}_{2}$

Step-by-step solution

{c}_{av} = \sqrt{\dfrac{8RT}{\piM}}; {c}_{mp} = \sqrt{\dfrac{2RT}{M}}

Given that,

\sqrt{\dfrac{8R{T}_{1}}{\pi{M}_{1}}} = \sqrt{\dfrac{2R{T}_{2}}{{M}_{2}}}

\dfrac{8{T}_{1}}{\pi{M}_{1}} = \dfrac{2{T}_{2}}{{M}_{2}}

\dfrac{4{T}_{1}}{\pi \times 56} = \dfrac{{T}_{2}}{44}

\dfrac{{T}_{1}}{{T}_{2}} = \dfrac{56 \times \pi}{44 \times 4} = 1

{T}_{1} = {T}_{2}

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