MHT CET · Physics · Thermodynamics
The initial pressure and volume of a gas is ' \(\mathrm{P}\) ' and ' \(\mathrm{V}\) ' respectively. First by isothermal process gas is expanded to volume ' \(9 \mathrm{~V}\) ' and then by adiabatic process its volume is compressed to ' \(\mathrm{V}\) ' then its final pressure is (Ratio of specific heat at constant pressure to constant volume \(=\frac{3}{2}\) )
- A \(6 \mathrm{~A}\)
- B 27P
- C 3P
- D 9P
Answer & Solution
Correct Answer
(C) 3P
Step-by-step Solution
Detailed explanation
\(\frac{C_p}{C_v}=\frac{3}{2}\)
Case I:
Isothermal process
\(
\begin{aligned}
& \mathrm{P}_1 \mathrm{~V}_1=\mathrm{P}_2 \mathrm{~V}_2 \\
& \mathrm{PV}=\mathrm{P}_2 \times 9 \mathrm{~V} \\
& \therefore \mathrm{P}_2=\frac{\mathrm{P}}{9}
\end{aligned}
\)
Case II: Adiabatic process
\(
\begin{aligned}
& \mathrm{P}_2 \mathrm{~V}_2^\gamma=\mathrm{P}_3 \mathrm{~V}_3^\gamma \\
& \frac{\mathrm{P}}{9}(9 \mathrm{~V})^\gamma=\mathrm{P}_3(\mathrm{~V})^\gamma \\
& \mathrm{P}_3=\left(\frac{\mathrm{P}}{9}\right) 9^\gamma=\left(\frac{\mathrm{P}}{9}\right) 9^{3 / 2}=\frac{\mathrm{P}}{9} \times 27=3 \mathrm{P}
\end{aligned}
\)
Case I:
Isothermal process
\(
\begin{aligned}
& \mathrm{P}_1 \mathrm{~V}_1=\mathrm{P}_2 \mathrm{~V}_2 \\
& \mathrm{PV}=\mathrm{P}_2 \times 9 \mathrm{~V} \\
& \therefore \mathrm{P}_2=\frac{\mathrm{P}}{9}
\end{aligned}
\)
Case II: Adiabatic process
\(
\begin{aligned}
& \mathrm{P}_2 \mathrm{~V}_2^\gamma=\mathrm{P}_3 \mathrm{~V}_3^\gamma \\
& \frac{\mathrm{P}}{9}(9 \mathrm{~V})^\gamma=\mathrm{P}_3(\mathrm{~V})^\gamma \\
& \mathrm{P}_3=\left(\frac{\mathrm{P}}{9}\right) 9^\gamma=\left(\frac{\mathrm{P}}{9}\right) 9^{3 / 2}=\frac{\mathrm{P}}{9} \times 27=3 \mathrm{P}
\end{aligned}
\)
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
- Magnetic flux passing through a coil is initially \(4 \times 10^{-4} Wb\). It reduces to \(10 \%\) of its original value in \(t\) second. If the emf induced is 0.72 mV then \(t\) in second isMHT CET 2016 Medium
- The time taken by a particle executing simple harmonic motion of period \(T\) to move from the mean position to half the maximum displacement isMHT CET 2022 Medium
- If dielectric is inserted in charged capacitor (battery removed), then quantity that remains constant isMHT CET 2009 Medium
- Two nuclei have their mass numbers in the ratio of \(1: 3\). The ratio of their nuclear densities would beMHT CET 2008 Hard
- The capacitance of a parallel plate capacitor is \(2.5 \mu \mathrm{F}\). When it is half filled with a dielectric as shown in figure, its capacitance becomes \(5 \mu \mathrm{F}\). The dielectric constant of the dielectric is
MHT CET 2023 Medium - A coil has inductance 2 H . The ratio of its reactance when it is connected first to an a.c. source and then to a d.c. source isMHT CET 2025 Easy
More PYQs from MHT CET
- For reaction \(\mathrm{A}+\mathrm{B} \rightarrow\) product, rate of reaction is \(3.6 \times 10^{-2} \mathrm{sec}^{-1}\). When \(\left[A^{\circ}\right]=0.2 \mathrm{moldm}^{-3}\) and \([B]=0.1 \mathrm{moldm}^{-3}\), calculate rate constant of reaction if reaction is first order in A and second order is B ?MHT CET 2024 Easy
- At \(300 \mathrm{~K}, 22 \mathrm{~g}\) of \(\mathrm{CO}_2\) gas exerts a pressure of 5 atmosphere. What is volume of the gas at same temperature?
\(\left(\mathrm{R}=0.0821 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)\)MHT CET 2021 Medium - \(\cos \left[\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)\right]=\)MHT CET 2024 Medium
- Calculate work done if 1 mole of an ideal gas expands isothermally from \(2 \mathrm{dm}^3\) to \(2.8 \mathrm{dm}^3\) against constant external pressure 1 atmMHT CET 2025 Medium
- If the lines \(\frac{1-x}{2}=\frac{7 y+4}{2 \lambda}=\frac{2 z-5}{2}\) and \(\frac{7-7 x}{3 \lambda}=\frac{y-1}{7}=\frac{6-z}{5}\) are at right angle, then the value of \(\lambda\) isMHT CET 2025 Medium
- An inductor may store energy inMHT CET 2012 Easy