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JEE Main 20208 JanuaryEvening Shift
Exam
JEE Main
Year
2020
Date
8 January
Shift
Evening Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2020 · 8 January · Evening Shift · Physics · Kinetic Theory of Gases

Consider a mixture of n moles of helium gas and 2n moles of oxygen...

Consider a mixture of nn moles of helium gas and 2n2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its CPCV\dfrac{{C}_{P}}{{C}_{V}} value will be:

Options

  1. A1913\dfrac{19}{13}
  2. B6745\dfrac{67}{45}
  3. C4027\dfrac{40}{27}
  4. D2315\dfrac{23}{15}

Correct answer

A. 1913\dfrac{19}{13}

Step-by-step solution

γ\gammamix =n1cp1+n2cp2n1cv1+n2cv2= \dfrac{{n}_{1}{c}_{{p}_{1}} + {n}_{2}{c}_{{p}_{2}}}{{n}_{1}{c}_{{v}_{1}} + {n}_{2}{c}_{{v}_{2}}}
=n(52R)+2n(72R)n(32R)+2n(52R)= \dfrac{n\left(\dfrac{5}{2}R\right) + 2n\left(\dfrac{7}{2}R\right)}{n\left(\dfrac{3}{2}R\right) + 2n\left(\dfrac{5}{2}R\right)}
=5+143+10=1913= \dfrac{5 + 14}{3 + 10} = \dfrac{19}{13}
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