MHT CET · Physics · Kinetic Theory of Gases
A gas at N.T.P. is suddenly compressed to \(\left(\frac{1}{4}\right)^{\mathrm{th}}\) of its original volume. The final pressure in (Given \(\gamma=\) ratio of sp. heats \(=\frac{3}{2}\) ) atmosphere is ( \(\mathrm{P}=\) original pressure \()\)
- A \(4\ P\)
- B \(\frac {3}{2}\ P\)
- C \(8\ P\)
- D \(\frac {1}{4}\ P\)
Answer & Solution
Correct Answer
(C) \(8\ P\)
Step-by-step Solution
Detailed explanation
In Adiabatic compression, \(\mathrm{PV}^\psi=\) constant
Given \(\mathrm{V}_{\text {new }}=\frac{1}{4} \mathrm{~V}\) and \(\gamma=\frac{3}{2}\)
\(\begin{aligned}
& \therefore \quad \frac{\mathrm{P}_{\mathrm{new}}}{\mathrm{P}}=\left(\frac{\mathrm{V}}{\mathrm{V}_{\text {new }}}\right)^7=\left(\frac{\mathrm{V}}{\frac{1}{4} \mathrm{~V}}\right)^{3 / 2} \\
& \therefore \quad \mathrm{P}_{\mathrm{new}}=8 \mathrm{P}
\end{aligned}\)
Given \(\mathrm{V}_{\text {new }}=\frac{1}{4} \mathrm{~V}\) and \(\gamma=\frac{3}{2}\)
\(\begin{aligned}
& \therefore \quad \frac{\mathrm{P}_{\mathrm{new}}}{\mathrm{P}}=\left(\frac{\mathrm{V}}{\mathrm{V}_{\text {new }}}\right)^7=\left(\frac{\mathrm{V}}{\frac{1}{4} \mathrm{~V}}\right)^{3 / 2} \\
& \therefore \quad \mathrm{P}_{\mathrm{new}}=8 \mathrm{P}
\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- The fundamental frequency of open pipe is 'n'. If it is closed from one end then frequency of the \(2^{\text {nd }}\) harmonic of closed pipe is higher by \(200 \mathrm{~Hz}\) than \({ }^{\prime} \mathrm{n}^{\prime}\). The value of 'n' isMHT CET 2020 Easy
- A small planet is revolving around a very massive star in a circular orbit of radius ' \(R\) ' with a period of revolution ' \(T\) '. If the gravitational force between the planet and the star were proportional to ' \(\mathrm{R}{ }^{-5 / 2}\), then ' T ', would be proportional toMHT CET 2024 Medium
- An e.m.f. \(\mathrm{E}=\mathrm{E}_{0} \sin \omega \mathrm{t}\) is applied to a circuit containing 'L' and 'R' in series. If \(X_{L}=R\), then the power dissipated in the circuit isMHT CET 2020 Easy
- In a biprism experiment, monochromatic light of wavelength ' \(\gamma\) ' is used. The distance between the two coherent sources ' \(d\) ' is kept constant. If the distance between slit and eyepiece ' \(D\) ' is varied as \(\mathrm{D}_1, \mathrm{D}_2, \mathrm{D}_3, \mathrm{D}_4\) and corresponding measured fringe widths are \(\mathrm{W}_1, \mathrm{~W}_2, \mathrm{~W}_3, \mathrm{~W}_4\) thenMHT CET 2024 Easy
- A magnetic field of \(2 \times 10^{-2} \mathrm{~T}\) acts at right angles to a coil of area \(100 \mathrm{~cm}^2\) with 50 turns. The average e.m.f. induced in the coil is \(0.1 \mathrm{~V}\), when it is removed from the field in time ' \(t\) '. The value of ' \(t\) ' isMHT CET 2023 Medium
- If ' \(\lambda_1\) ' and ' \(\lambda_2\) ' are the wavelengths of the first member of the Balmer and Paschen series, in hydorgen atom respectively, then the ratio of respective frequencies, \(f_1 / f_2\), isMHT CET 2025 Medium
More PYQs from MHT CET
- The numbers of turns in the primary and the secondary of a transformer are 1000 and 3000 respectively. If \(80 \mathrm{~V}\) a.c. is applied to the primary coil of the transformer, then the potential difference per turn of the secondary coil would beMHT CET 2023 Medium
- The abscissa of the point on the curve \(y=\mathrm{a}\left(\mathrm{e}^{\frac{x}{a}}+\mathrm{e}^{-\frac{x}{a}}\right)\) where the tangent is parallel to the X -axis isMHT CET 2024 Medium
- A prism having refractive index \(\sqrt{2}\) and refracting angle \(30^{\circ}\) has one of the
refracting surfaces silvered. The beam of light incident on the other refracting
surface will retrace its path, if angle of incidence is \(\left[\sin \frac{\pi}{6}=0 \cdot 5\right]\)MHT CET 2020 Medium - We have a sample of gas characterised by \(\mathrm{P}, \mathrm{V}\) and \(\mathrm{T}\) and another sample of gas characterised by \(2 \mathrm{P}, \mathrm{V} / 4\), and \(2 \mathrm{~T}\). What is the ratio of the number of molecules in the first and second samples?MHT CET 2020 Easy
- Identify the major product when anisole is treated with \(\mathrm{Br}_2\) in presence of acetic acid.MHT CET 2021 Hard
- With usual notations, in \(\triangle \mathrm{ABC}\), if \(\mathrm{a}=2, \mathrm{~b}=3, \mathrm{c}=5\) and \(\frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=\frac{k+7}{30}\),
then \(\mathrm{k}=\)MHT CET 2020 Hard