JEE Mains · Physics · STD 11 - 11. thermodynamics
A sample of gas at temperature \(\mathrm{T}\) is adiabatically expanded to double its volume. Adiabatic constant for the gas is \(\gamma=3 / 2\). The work done by the gas in the process is _______. \((\mu=1 \mathrm{~mole})\)
- A \(\mathrm{RT}[\sqrt{2}-2]\)
- B \(\mathrm{RT}[1-2 \sqrt{2}]\)
- C \(\mathrm{RT}[2 \sqrt{2}-1]\)
- D \(\mathrm{RT}[2-\sqrt{2}]\)
Answer & Solution
Correct Answer
(D) \(\mathrm{RT}[2-\sqrt{2}]\)
Step-by-step Solution
Detailed explanation
\(\mathrm{W}=\frac{\mathrm{nR} \Delta \mathrm{T}}{1-\gamma}\) \(\mathrm{TV}^{\gamma-1}=\text { constant }=\mathrm{T}_{\mathrm{f}}(2 \mathrm{~V})^{\gamma-1}\) \(\mathrm{~T}_{\mathrm{f}}=\mathrm{T}\left(\frac{1}{2}\right)^{1 / 2}=\frac{\mathrm{T}}{\sqrt{2}}\)…
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
- A long solenoid is formed by winding \(70\) turns \(cm ^{-1}\). If \(2.0\,A\) current flows, then the magnetic field produced inside the solenoid is \(.......\times 10^{-4}\,T\) \(\left(\mu_0=4 \pi \times 10^{-7}\,TmA ^{-1}\right)\)JEE Mains 2023 Easy
- The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at \(V _{ Z }=5 V\) and the desired current in load is 5 mA . The unregulated voltage source can supply upto 25 V . Considering the Zener diode can withstand four times of the load current, the value of resistor \(R _{ S }\) (shown in circuit) should be ___________ \(\Omega\).
JEE Mains 2026 Easy - An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at \(30°\) and \(90°\), respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at \(60°\) with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is ______.JEE Mains 2026 Hard
- Using Young's double slit experiment, a monochromatic light of wavelength \(5000\,\mathring A\) produces fringes of fringe width \(0.5 \,mm\). If another monochromatic light of wavelength \(6000\,\mathring A\) is used and the separation between the slits is doubled, then the new fringe width will be ............... \(mm\)JEE Mains 2022 Hard
- In the given circuit diagram, a wire is joining points \(B\) and \(D\). The current in this wire is ............. \(A\)
JEE Mains 2020 Medium - A swimmer can swim with velocity of \(12 \,km / h\) in still water. Water flowing in a river has velocity \(6\, km / h\). The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ........\(^{\circ}\). (Round off to the Nearest Integer) (find the angle in degree)JEE Mains 2021 Hard
More PYQs from JEE Mains
- Let \(N\) denotes the sum of the numbers obtained when two dice are rolled. If the probability that \(2^{ N } < N !\) is \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, then \(4 m -3 n\) is equal to \(......\).JEE Mains 2023 Hard
- If a rectangle is inscribed in an equilateral triangle of side length \(2 \sqrt{2}\) as shown in the figure, then the square of the largest area of such a rectangle is \(....\)
JEE Mains 2021 Hard - If the equation \(\cos ^{4} \theta+\sin ^{4} \theta+\lambda=0\) has real solutions for \(\theta,\) then \(\lambda\) lies in the intervalJEE Mains 2020 Hard
- A particle of mass \(m\) is moving in a straight line with momentum \(p\). Starting at time \(t = 0\), a force \(F = kt\) acts in the same direction on the moving particle during time interval \(T\) so that its momentum changes from \(p\) to \(3p\). Here \(k\) is a constant. The value of \(T\) isJEE Mains 2019 Medium
- Let \(\overrightarrow{\mathrm{a}}=3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{c}}\) be a vector such that \((\vec{a}+\vec{b}) \times \vec{c}=2(\vec{a} \times \vec{b})+24 \hat{j}-6 \hat{k}\) and \((\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}+\hat{\mathrm{i}}) \cdot \overrightarrow{\mathrm{c}}=-3\). Then \(|\overrightarrow{\mathrm{c}}|^2\) is equal to ...........JEE Mains 2024 Hard
- Let \(A\) and \(B\) be two non -null events such that \(A \subset B\). Then, which of the following statements is always correct?JEE Mains 2019 Hard