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Waves question

2015 · Q109
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Waves question

2015 · Q109

NEETPhysicsWavesMCQ+4 / −1
4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K−-−1 mol−-−1. If the speed of sound in this gas at NTP is 952 m s−-−1, then the heat capacity at constant pressure is
(Take gas constant R === 8.3 J K−-−1 mol−-−1)
  1. A
    7.0 J K−-−1 mol−-−1
  2. B
    8.5 J K−-−1 mol−-−1
  3. C
    8.0 J K−-−1 mol−-−1
  4. D
    7.5 J K−-−1 mol−-−1
View written solutionFree

Correct answer: C

Molar mass of the gas = 4g/mol
Speed of sound

V=γRTm⇒952=γ×3.3×2734×10−3V = \sqrt {{{\gamma RT} \over m}} \Rightarrow 952 = \sqrt {{{\gamma \times 3.3 \times 273} \over {4 \times {{10}^{ - 3}}}}} V=mγRT​​⇒952=4×10−3γ×3.3×273​​

⇒γ=1.6=1610=85 \Rightarrow \gamma = 1.6 = {{16} \over {10}} = {8 \over 5}⇒γ=1.6=1016​=58​

Also, γ=CPCV=85\gamma = {{{C_P}} \over {{C_V}}} = {8 \over 5}γ=CV​CP​​=58​

⇒CP=8×55=8 JK−1mol−1 \Rightarrow {C_P} = {{8 \times 5} \over 5} = 8\,J{K^{ - 1}}mo{l^{ - 1}}⇒CP​=58×5​=8JK−1mol−1
[CV = 5.0 JK–1 given]

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