JEE Mains · Physics · STD 11 - Thermodynamics
- JEE Mains 2026
- Medium
- MCQ
Initial pressure and volume of a monoatomic ideal gas are \(P\) and \(V\). The change in internal energy of this gas in adiabatic expansion to volume \(V_{final}=27V\) is ________ J.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(-\dfrac{4}{3}PV\)
Step-by-step Solution
Detailed explanation
For a monoatomic ideal gas, the ratio of specific heats is \(\gamma = \dfrac{5}{3}\).
In an adiabatic process, \(PV^{\gamma} = \text{constant}\).
\(P_1 V_1^{\gamma} = P_2 V_2^{\gamma}\)
\(P V^{5/3} = P_2 (27V)^{5/3}\)
\(P_2 = P \left(\dfrac{1}{27}\right)^{5/3} = \dfrac{P}{243}\)
The change in internal energy is given by:
\(\Delta U = \dfrac{P_2 V_2 - P_1 V_1}{\gamma - 1}\)
Substituting the values:
\(\Delta U = \dfrac{\left(\dfrac{P}{243}\right)(27V) - PV}{\dfrac{5}{3} - 1}\)
\(\Delta U = \dfrac{\dfrac{PV}{9} - PV}{\dfrac{2}{3}}\)
\(\Delta U = \dfrac{-\dfrac{8}{9}PV}{\dfrac{2}{3}} = -\dfrac{4}{3}PV\)
Answer: \(-\dfrac{4}{3}PV\)
In an adiabatic process, \(PV^{\gamma} = \text{constant}\).
\(P_1 V_1^{\gamma} = P_2 V_2^{\gamma}\)
\(P V^{5/3} = P_2 (27V)^{5/3}\)
\(P_2 = P \left(\dfrac{1}{27}\right)^{5/3} = \dfrac{P}{243}\)
The change in internal energy is given by:
\(\Delta U = \dfrac{P_2 V_2 - P_1 V_1}{\gamma - 1}\)
Substituting the values:
\(\Delta U = \dfrac{\left(\dfrac{P}{243}\right)(27V) - PV}{\dfrac{5}{3} - 1}\)
\(\Delta U = \dfrac{\dfrac{PV}{9} - PV}{\dfrac{2}{3}}\)
\(\Delta U = \dfrac{-\dfrac{8}{9}PV}{\dfrac{2}{3}} = -\dfrac{4}{3}PV\)
Answer: \(-\dfrac{4}{3}PV\)
More questions from Physics
- The radius of \(2^{\text {nd }}\) orbit of \(He ^{+}\)of Bohr's model is \(r _1\) and that of fourth orbit of \(Be ^{3+}\) is represented as \(r _2\). Now the ratio \(\frac{r_2}{r_1}\) is \(x : 1\). The value of \(x\) is .........JEE Mains 2023 Medium
- In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is \(2.4\) \(\mu\)m. If the experiment is carried out in another medium having refractive index \(1.2\), the fringe width will be _____ \(\mu\)m.JEE Mains 2026 Easy
- In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.JEE Mains 2021 Medium
- If force \(({F})\), length \(({L})\) and time \(({T})\) are taken as the fundamental quantities. Then what will be the dimension of densityJEE Mains 2021 Hard
- In a screw gauge, \(5\) complete rotations of the screw cause it to move a linear distance of \(0.25\, cm\). There are \(100\) circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of \(4\) main scale divisions and \(30\) circular scale divisions . Assuming negligible zero error, the thickness of the wire isJEE Mains 2018 Medium
- The moment of inertia of semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is \(\frac{1}{ x } MR ^2\), where \(R\) is the radius and \(M\) is the mass of semicircular ring. The value of \(x\) will be \(...........\)JEE Mains 2023 Easy
More PYQs from JEE Mains
- If an emitter current is changed by \(4\, mA ,\) the collector current changes by \(3.5\, mA\). The value of \(\beta\) will beJEE Mains 2021 Medium
- The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) :
JEE Mains 2025 Hard - A force on an object of mass \(100\, g\) is \((10 \hat{i}+5 \hat{j}) N\). The position of that object at \(t=\) \(2 s\) is \((a \hat{i}+b \hat{j}) m\) after starting from rest. The value of \(\frac{a}{b}\) will be..........JEE Mains 2022 Medium
- For particle \(P\) revolving round the centre \(O\) with radius of circular path \(r\) and angular velocity \(\omega\), as shown in below figure, the projection of \(OP\) on the \(x\)-axis at time \(t\) is \(.................\).
JEE Mains 2023 Easy