JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
The equation for real gas is given by \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where \(\mathrm{P}, \mathrm{V}, \mathrm{T}\) and R are the pressure, volume, temperature and gas constant, respectively. The dimension of \(\mathrm{ab}^{-2}\) is equivalent to that of :
- A Planck's constant
- B Compressibility
- C Strain
- D Energy density
Answer & Solution
Correct Answer
(D) Energy density
Step-by-step Solution
Detailed explanation
\begin{aligned} & {\left[\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right](\mathrm{V}-\mathrm{b})=\mathrm{RT}} \\ & \therefore[\mathrm{a}]=[\mathrm{P}]\left[\mathrm{V}^2\right]=\mathrm{ML}^{-1} \mathrm{~T}^{-2} \mathrm{~L}^6=\mathrm{ML}^5 \mathrm{~T}^{-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
- Ship \(A\) is sailing towards north -east with velocity \(\vec v = 30\,\hat i + 50\hat j\,km/hr\) where \(\hat i\) points east and \(\hat j\) , north. Ship \(B\) is at a distance of \(80\, km\) east and \(150\, km\) north of Ship \(A\) and is sailing towards west at \(10\, km/hr\). \(A\) will be at minimum distance from \(B\) is.........\(hrs\)JEE Mains 2019 Hard
- A uniform solid cylindrical roller of mass \('m'\) is being pulled on a horizontal surface with force \(F\) parallel to the surface and applied at its centre. If the acceleration of the cylinder is \('a'\) and it is rolling without slipping then the value of \('F'\) isJEE Mains 2015 Hard
- An electron of mass \(m\) is moving in an electric field \(\vec{E} = -2E_0\hat{i}\) (\(E_0 =\) constant \(> 0\)), with an initial velocity \(\vec{V} = v_0\hat{i}\) (\(v_0 =\) constant \(> 0\)). If \(\lambda_0 = \dfrac{h}{4mv_0}\), its de Broglie wavelength at time \(t\) is __________.
(\(e =\) charge of electron)JEE Mains 2026 Hard - Match List \(− I\) (Event) with List \(−II \) (Order of the time interval for happening of the event) and select the correct option from the options given below the lists
List \(- I\) List \(- II\) \((1)\) Rotation period of earth \((i)\) \(10^5\, s\) \((2)\) Revolution period of earth \((ii)\) \(10^7\, s\) \((3)\) Period of light wave \((iii)\) \(10^{-15}\, s\) \((4)\) Period of sound wave \((iv)\) \(10^{-3}\, s\) JEE Mains 2014 Medium - An ideal gas initially at \(0^{\circ} \mathrm{C}\) temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is \(3 / 2\), the change in temperature due to the thermodynamic process is _____ K.JEE Mains 2025 Medium
- A sample of gas expands from \(V_1\) to \(V _2\). In which of the following, the work done will be greatest ?
JEE Mains 2013 Medium
More PYQs from JEE Mains
- Moment of Inertia \((M.I.)\) of four bodies having same mass ' \(M\) ' and radius ' \(2 R^{\prime}\) are as follows \(I _{1}=\) \(M.I.\) of solid sphere about its diameter \(I _{2}=\) \(M.I.\) of solid cylinder about its axis \(I _{3}=\) \(M.I.\) of solid circular disc about its diameter \(I _{4}=\) \(M.I.\) of thin circular ring about its diameter If \(2\left(I_{2}+I_{3}\right)+I_{4}=x\). \(I_{1}\) then the value of \(x\) will be.......JEE Mains 2022 Medium
- Out of \(60 \%\) female and \(40 \%\) male candidates appearing in an exam, \(60\%\) candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is.JEE Mains 2022 Medium
- Two identical parallel plate capacitors, of capacitance \(C\) each, have plates of area \(A\), separated by a distance \(d\). The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants \(K_1\) , \(K_2\) and \(K_3\) . The first capacitor is filled as shown in fig. \(I\), and the second one is filled as shown in fig. \(II\). If these two modified capacitors are charged by the same potential \(V\), the ratio of the energy stored in the two, would be ( \(E_1\) refers to capacitor \((I)\) and \(E_2\) to capacitor \((II)\))
JEE Mains 2019 Hard - Let \( \alpha, \beta \) be the roots of the quadratic equation \( 12x^{2}-20x+3\lambda=0, \lambda\in\mathbb{Z} \). If \( \frac{1}{2}\le|\beta-\alpha|\le\frac{3}{2}, \) then the sum of all possible values of \( \lambda \) is :JEE Mains 2026 Medium
- Consider the circle \(\mathrm{C}: \mathrm{x}^2+\mathrm{y}^2=4\) and the parabola \(P: y^2=8 x\). If the set of all values of \(\alpha\), for which three chords of the circle \(\mathrm{C}\) on three distinct lines passing through the point \((\alpha, 0)\) are bisected by the parabola \(P\) is the interval \((p, q)\), then \((2 q-p)^2\) is equal to .............JEE Mains 2024 Hard
- In the truth table of the above circuit the value of \(\mathrm{X}\) and \(\mathrm{Y}\) are _______.
JEE Mains 2024 Hard