MHT CET · Physics · Kinetic Theory of Gases
We have a jar filled with gas characterized by parameters \(\mathrm{P}, \mathrm{V}, \mathrm{T}\) and another jar B filled with gas having parameters \(2 \mathrm{P}, \frac{\mathrm{V}}{4}, 2 \mathrm{~T}\), where symbols have their usual meaning. The ratio of number of molecules in jar A to those in jar B is
- A \(1: 1\)
- B \(1: 2\)
- C \(2: 1\)
- D \(4: 1\)
Answer & Solution
Correct Answer
(D) \(4: 1\)
Step-by-step Solution
Detailed explanation
According to the gas equation, \(\mathrm{PV}=\mathrm{Nk}_{\mathrm{B}} \mathrm{T}\) For the first gas, we have,
\(\mathrm{PV}=\mathrm{N}_1 \mathrm{k}_{\mathrm{B}} \mathrm{T}\)
For the second gas, we have,
(2P) \(\left(\frac{\mathrm{V}}{4}\right)=\mathrm{N}_2 \mathrm{k}_{\mathrm{B}}(2 \mathrm{~T})\)
\(\mathrm{PV}=4 \mathrm{~N}_2 \mathrm{k}_{\mathrm{B}} \mathrm{T}\)
From equations (i) and (ii)
\(\mathrm{N}_1=4 \mathrm{~N}_2 \Rightarrow \frac{\mathrm{N}_1}{\mathrm{~N}_2}=4\)
\(\mathrm{PV}=\mathrm{N}_1 \mathrm{k}_{\mathrm{B}} \mathrm{T}\)
For the second gas, we have,
(2P) \(\left(\frac{\mathrm{V}}{4}\right)=\mathrm{N}_2 \mathrm{k}_{\mathrm{B}}(2 \mathrm{~T})\)
\(\mathrm{PV}=4 \mathrm{~N}_2 \mathrm{k}_{\mathrm{B}} \mathrm{T}\)
From equations (i) and (ii)
\(\mathrm{N}_1=4 \mathrm{~N}_2 \Rightarrow \frac{\mathrm{N}_1}{\mathrm{~N}_2}=4\)
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
- When a mercury drop of radius 'R', breaks into 'n' droplets of equal size, the radius 'r' of each droplet isMHT CET 2020 Easy
- A beam of light of wavelength \(600 \mathrm{~nm}\) from a distant source falls on a single slit \(1 \mathrm{~mm}\) wide and the resulting diffraction pattern is observed on a screen \(2 \mathrm{~m}\) away. The distance between the first dark fringe on either side of the central bright fringe isMHT CET 2023 Medium
- In the following network, the current through galvanometer will
MHT CET 2022 Hard - Two copper wires of radii \(r_1\) and \(r_2\left(r_1>r_2\right)\) are subjected to the same tension and are plucked. The transverse waves willMHT CET 2022 Easy
- Heat engine operating between temperature \(T_1\) and \(T_2\) has efficiency \(\frac{1}{6}\). When \(T_2\) is lowered by 62 K , its efficiency increases to \(\frac{1}{3}\). Then \(\mathrm{T}_1\) and \(\mathrm{T}_2\) respectively areMHT CET 2024 Medium
- Two identical long parallel wires carry currents \(I_1\) and \(I_2\) such that \(I_1>I_2\). When the currents are in the same direction, the magnetic field at a point midway between the wires is \(6 \times 10^{-6} \mathrm{~T}\). If the direction of \(I_2\) is reversed, the field becomes \(3 \times 10^{-5} \mathrm{~T}\). The ratio \(\left(\frac{I_1}{I_2}\right)\) is-MHT CET 2022 Hard
More PYQs from MHT CET
- Four electric charges \(+\mathrm{q},+\mathrm{q},-\mathrm{q}\) and \(-\mathrm{q}\) are placed in order at the corners of a square of side \(2 \mathrm{~L}\). The electric potential at point midway between the two positive charges isMHT CET 2021 Medium
- An a.c. source is applied to a series LR circuit with \(X_L=3 R\) and power factor is \(X_1\). Now a capacitor with \(X_C=R\) is added in series to LR circuit and the power factor is \(X_2\). The ratio \(X_1\) to \(X_2\) isMHT CET 2025 Medium
- Two conducting circular loops of radii ' \(\mathrm{R}_1\) ' and ' \(R_2\) ' are placed in the same plane with their centres coinciding. If \(\mathrm{R}_1>\mathrm{R}_2\), the mutual inductance \(\mathrm{M}\) between them will be directly proportional toMHT CET 2023 Hard
- Which of the following species has highest mass?MHT CET 2022 Medium
- If enthalpy change for following reaction at \(300 \mathrm{~K}\) is \(+7 \mathrm{~kJ} \mathrm{~mol}^{-1}\) find the entropy change of surrounding?
\(\mathrm{H}_2 \mathrm{O}_{(\mathrm{s})} \longrightarrow \mathrm{H}_2 \mathrm{O}_{(l)}\)MHT CET 2023 Easy - In which of the following salts, the solubility increases appreciably with increase in temperature?MHT CET 2021 Hard