JEE Main 2025 (Online) 4th April Morning Shift | Heat and Thermodynamics Question 12 | Physics

Consider the sound wave travelling in ideal gases of $\mathrm{He}, \mathrm{CH}_4$, and $\mathrm{CO}_2$. All the gases have the same ratio $\frac{P}{\rho}$, where $P$ is the pressure and $\rho$ is the density. The ratio of the speed of sound through the gases $\mathrm{V}_{\mathrm{He}}: \mathrm{V}_{\mathrm{CH}_4}: \mathrm{V}_{\mathrm{CO}_2}$ is given by

$\sqrt{\frac{7}{5}}: \sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}$

$\sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}: \sqrt{\frac{4}{3}}$

$\sqrt{\frac{5}{3}}: \sqrt{\frac{4}{3}}: \sqrt{\frac{7}{5}}$

$\sqrt{\frac{4}{3}}: \sqrt{\frac{5}{3}}: \sqrt{\frac{7}{5}}$

JEE Main 2025 (Online) 4th April Morning Shift

MCQ (Single Correct Answer)

-1

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3 \times 10^{-7} \mathrm{~m}$ and $600 \mathrm{~m} / \mathrm{s}$, respectively. Find the frequency of its collisions.

$$5 \times 10^8 / \mathrm{s}$$

$9 \times 10^5 / \mathrm{s}$

$2 \times 10^{10} / \mathrm{s}$

$2 \times 10^9 / \mathrm{s}$

JEE Main 2025 (Online) 3rd April Evening Shift

MCQ (Single Correct Answer)

-1

An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to 4 times of its initial volume $\left(\mathrm{V}_0\right)$, then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

$\mathrm{P}_0 \mathrm{~V}_0(\ln 2-0.75)$

$\mathrm{P}_0 \mathrm{~V}_0(2 \ln 2-0.75)$

$\mathrm{P}_0 \mathrm{~V}_0(2 \ln 2-0.25)$

$\mathrm{P}_0 \mathrm{~V}_0(\ln 2-0.25)$

JEE Main 2025 (Online) 3rd April Evening Shift

MCQ (Single Correct Answer)

-1

Pressure of an ideal gas, contained in a closed vessel, is increased by $0.4 \%$ when heated by $1^{\circ} \mathrm{C}$. Its initial temperature must be:

2500 K

$25^{\circ} \mathrm{C}$

$250^{\circ} \mathrm{C}$

250 K

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