JEE Mains · Physics · STD 11 - Kinetic theory of gases
- JEE Mains 2019
- Hard
- MCQ
The specific heats, \(C_P\) and \(C_V\) of a gas of diatomic molecules, \(A\), are given (in units of \(J\, mol^{-1}\, K^{-1}\)) by \(29\) and \(22\), respectively. Another gas of diatomic molecules \(B\), has the corresponding values \(30\) and \(21\). If they are treated as ideal gases, then
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(A\) has a vibrational mode but \(B\) has none
Step-by-step Solution
Detailed explanation
For \(A:\)
\(\frac{C_{p}}{C_{v}}=\gamma=1+\frac{2}{f}=\frac{29}{22}\)
It gives \(f=6.3 \approx 6 \quad(3 \text { translational, } 2 \text { rotational and } 1\) vibrational)
For \(B:\)
\(\frac{C_{p}}{C_{v}}=\gamma=1+\frac{2}{f}=\frac{30}{21}\)
\(\Rightarrow \mathrm{f}=4.67\)
\(\Rightarrow \quad \approx 5 \quad(3 \text { translational, } 2\) rotational, no vibrational)
More questions from Physics
- A \(12\,V\) battery connected to a coil of resistance \(6 \,\Omega\) through a switch, drives a constant current in the circuit. The switch is opened in \(1\,ms\). The emf induced across the coil is \(20 \;V\). The inductance of the coil is ........... \(mH\)JEE Mains 2023 Medium
- The angular momentum for the electron in Bohr's orbit is \(L\). If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will beJEE Mains 2023 Medium
- The magnetic field of earth at the equator is approximately \(4 \times 10^{-5}\, T\) . The radius of earth is \(6.4 \times 10^6\, m\). Then the dipole moment of the earth will be nearly of the order ofJEE Mains 2014 Medium
- A train moves towards a stationary observer with speed \(34\, m/s\). The train sounds a whistle and its frequency registered by the observer is \(f_1\). If the speed of the train is reduced to \(17\, m/s\), the frequency registered is \(f_2\). If speed of sound is \(340\, m/s\), then the ratio \(f_1/f_2\) isJEE Mains 2019 Hard
- A star has \(100 \%\) helium composition. It starts to convert three \({ }^4 \mathrm{He}\) into one \({ }^{12} \mathrm{C}\) via triple alpha process as \({ }^4 \mathrm{He}+{ }^4 \mathrm{He}+{ }^4 \mathrm{He} \rightarrow{ }^{12} \mathrm{C}+\mathrm{Q}\). The mass of the star is \(2.0 \times 10^{32} \mathrm{~kg}\) and it generates energy at the rate of \(5.808 \times 10^{30} \mathrm{~W}\). The rate of converting these \({ }^4 \mathrm{He}\) to \({ }^{12} \mathrm{C}\) is \(\mathrm{n} \times 10^{42} \mathrm{~s}^{-1}\), where \(\mathrm{n}\) is _______. [Take, mass of \({ }^4 \mathrm{He}=4.0026 \mathrm{u}\), mass of \({ }^{12} \mathrm{C}=12 \mathrm{u}\)]JEE Mains 2024 Hard
- The elongation of a wire on the surface of the earth is \(10^{-4} \; m\). The same wire of same dimensions is elongated by \(6 \times 10^{-5} \; m\) on another planet. The acceleration due to gravity on the planet will be \(\dots \; ms ^{-2}\). (Take acceleration due to gravity on the surface of earth \(=10 \; m / s ^{-2}\) )JEE Mains 2022 Hard
