Kinetic Theory

JEE Main level, single correct, medium

104 of 168

Question 104 of 168

The specific heats, Cp{C}_{p} and Cv{C}_{v} of a gas of diatomic molecules, A,A, are given (in units of Jmol−1K−1Jmo{l}^{-1}{K}^{-1} ) by 2929 and 22,22, respectively. Another gas of diatomic molecules, B,B, has the corresponding values 3030 and 21.21. If they are treated as ideal gases, then:

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Answer: (B) AA has a vibrational mode but BB has none.

For AA :
R=Cp−Cv=29−22=7R={C}_{p}-{C}_{v}=29-22=7
Cv=fR2{C}_{v}=\dfrac{fR}{2}
⇒22=f×72\Rightarrow 22=\dfrac{f\times 7}{2}
⇒f=447=6.3\Rightarrow f=\dfrac{44}{7}=6.3
⇒f≈6\Rightarrow f\approx 6
(5 rotational + translational, 1 vibrational)

For BB :
R=Cp−CV=30−21=9R={C}_{p}-{C}_{V}=30-21=9
Cv=fR2=21{C}_{v}=\dfrac{fR}{2}=21
⇒f=21×29=429=4.66≃5\Rightarrow f=\dfrac{21\times 2}{9}=\dfrac{42}{9}=4.66≃5
∴f≃5∴ f≃5
(5 rotational + transitional, 0 vibrational)

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