Match Column -I and Column - II and choose the correct match from the given choices.

Option 1 -

(A) -(R), (B)-(P), (C)-(S), (D)-(Q)

Option 2 -

(A)-(Q), (R)-(R), (C)-(S), (D)-(P)

Option 3 -

(A)-(Q), (B)-(P), (C)-(S), (D)-(R)

Option 4 -

(A)-(R), (B)-(Q), (C)-(P), (D)-(S)

3 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

Root mean square speed of gas molecules

$ν_{rms} = \sqrt[]{\frac{3 R T}{M}}$

Pressure exerted by ideal Gas

$P = \frac{1}{3} ρ v_{r m s}^{2}$

$P = \frac{1}{3} m n ν^{2}$

$ρ = m n, v_{r m s}^{2} = ν^{- 2}$

Average kinetic energy of a molecular

$K E = \frac{3}{2} K T$

Total internal energy of 1 mole of a diatomic gas

$U = \frac{f}{2} μ R T$

$U = \frac{5}{2} R T$ (For 1 mole diatomic gas)

Root mean square speed of gas molecules <math> <msub> <mrow> <mrow> <mi>ν</mi> </mrow> </mrow> <mrow> <mrow> <mtext>rms</mtext> <mtext> </mtext> </mrow> </mrow> </msub> <mo>=</mo> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>3</mn> <mi>R</mi> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mi>M</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow></mrow> </mroot> </math> Pressure exerted by ideal Gas <math> <mi mathvariant="normal">P</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> <mi>ρ</mi> <msubsup> <mrow> <mrow> <mi>v</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> </math> <!- [endif]-><!- [endif]-> <math> <mi mathvariant="normal">P</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">n</mi> <msup> <mrow> <mrow> <mi>ν</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> <!- [endif]-><!- [endif]-> <math> <mi>ρ</mi> <mo>=</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">n</mi> <mo>, </mo> <msubsup> <mrow> <mrow> <mi mathvariant="normal">v</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msubsup> <mo>=</mo> <msup> <mrow> <mrow> <mi>ν</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </mrow> </msup> </math> <!- [endif]-><!- [endif]->Average kinetic energy of a molecular <math> <mi mathvariant="normal">K</mi> <mi mathvariant="normal">E</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi mathvariant="normal">K</mi> <mi mathvariant="normal">T</mi> </math> <!- [endif]-><!- [endif]->Total internal energy of 1 mole of a diatomic gas <math> <mi mathvariant="normal">U</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi>μ</mi> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">T</mi> </math> <!- [endif]-><!- [endif]-> <math> <mi mathvariant="normal">U</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">T</mi> </math> (For 1 mole diatomic gas)

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Match Column -I and Column - II and choose the correct match from the given choices.

1 Answer

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