A container is occupied by a fixed number of non-interacting particles. If they are obeying Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann statistics, the pressure in the container is PFD, PBE and PMB, respectively. Then
- PFD > PMB > PBE
- PFD > PMB = PBE
- PFD > PBE > PMB
- PFD = PMB = PBE
The Correct Option is A
Solution and Explanation
To solve this problem, we need to understand the differences between the three types of statistical mechanics: Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann.
- Fermi-Dirac Statistics (FD): This applies to particles known as fermions, which obey the Pauli exclusion principle, meaning no two identical fermions can occupy the same quantum state simultaneously. Electrons are a common example.
- Bose-Einstein Statistics (BE): This applies to particles known as bosons, which can occupy the same quantum state as others. Photons and helium-4 atoms in certain conditions can be described by such statistics.
- Maxwell-Boltzmann Statistics (MB): This describes the distribution of classical particles, or particles that do not obey quantum mechanical effects at the level relevant in Fermi-Dirac or Bose-Einstein statistics.
The key difference is that Fermi-Dirac statistics account for the quantum restrictions that prevent identical fermions from occupying the same state. This restriction generally leads to a higher pressure when compared to Maxwell-Boltzmann statistics, which do not consider such restrictions.
On the other hand, Bose-Einstein statistics allow for the accumulation of particles in the same state, leading to an overall tendency for lower pressures compared to Maxwell-Boltzmann pressures under certain conditions, particularly at low temperatures.
Therefore, based on these explanations:
- PFD: The pressure following Fermi-Dirac statistics will be the highest since the Pauli exclusion principle prevents too many fermions from occupying low energy states, increasing the system's pressure.
- PMB: This is the middle ground as it does not have any quantum restrictions like Fermi-Dirac, but neither does it allow overlap like Bose-Einstein.
- PBE: The lowest pressure results from Bose-Einstein statistics since particles can reside in the same state, reducing the system's pressure.
Thus, for the given container of particles, the pressures follow the relationship:
This matches the correct answer provided in your options.
Top Questions on Mechanics and General Properties of Matter
In order to achieve the static equilibrium of the see-saw about the fulcrum \( P \), shown in the figure, the weight of Box B should be _________ kg, if the weight of Box A is 50 kg.
- GATE AR - 2025
- Building Services and Sustainability
- Mechanics and General Properties of Matter
- An unstable particle created at a point P moves with a constant speed of 0.998c until it decays at a point Q. If the lifetime of the particle in its rest frame is 632ns, the distance between points P and Q is ______m. (Rounded off to the nearest integer)
(c=3×108 m/s)- IIT JAM PH - 2024
- Physics
- Mechanics and General Properties of Matter
- The moment of inertia of a solid hemisphere (mass 𝑀 and radius 𝑅) about the axis passing through the hemisphere and parallel to its flat surface is \(\frac{2}{5}\) 𝑀𝑅2 . The distance of the axis from the center of mass of the hemisphere (in units of 𝑅) is______. (Rounded off to two decimal places)
- IIT JAM PH - 2024
- Physics
- Mechanics and General Properties of Matter
A particle of mass 1kg, initially at rest, starts sliding down from the top of a frictionless inclined plane of angle \(\frac{𝜋}{6}\)\(\frac{\pi}{6}\) (as schematically shown in the figure). The magnitude of the torque on the particle about the point O after a time 2seconds is ______N-m. (Rounded off to nearest integer)
(Take g = 10m/s2)- IIT JAM PH - 2024
- Physics
- Mechanics and General Properties of Matter
- The inertial frame 𝑆' is moving away from the inertial frame S with a speed 𝑣 = 0.6𝑐 along the negative x-direction (see figure). The origins 𝑂’ and 𝑂 of the frames coincide at 𝑡=𝑡’=0. As observed in the frame 𝑆′, two events occur simultaneously at two points on the 𝑥′-axis with a separation of ∆𝑥′=5m. If, ∆𝑡 and ∆𝑥 are the magnitudes of the time interval and the space interval, respectively, between the events in S, then which of the following statements is(are) correct?
(c = 3×108 m/s)- IIT JAM PH - 2024
- Physics
- Mechanics and General Properties of Matter
Questions Asked in IIT JAM exam
- Consider a volume V enclosed by a closed surface S having unit surface normal \(\hat{n}\). For \(\mathbf{r} = x\hat{i} + y\hat{j} + z\hat{k}\), the value of the surface integral \(\frac{1}{9} \oint_{S} \mathbf{r} \cdot \hat{n} \,dS\) is
- IIT JAM PH - 2025
- Vector Calculus
- For a Zener diode as shown in the circuit diagram below, the Zener voltage \(V_Z\) is 3.7 V. For a load resistance (\(R_L\)) of 1 k\(\Omega\), a current \(I_1\) flows through the load. If \(R_L\) is decreased to 500 \(\Omega\), the current changes to \(I_2\). The ratio \(\frac{I_2}{I_1}\) is \rule{1cm{0.15mm}. (up to two decimal places)}
- IIT JAM PH - 2025
- Analog Electronics
- The shortest distance between an object and its real image formed by a thin convex lens of focal length 20 cm is _____ cm. (in integer)
- If \(\left(\frac{1-i}{1+i}\right)^{n/2} = -1\), where \(i = \sqrt{-1}\), one possible value of n is
- IIT JAM PH - 2025
- Complex numbers
- In a two-level atomic system, the excited state is 0.2 eV above the ground state. Considering the Maxwell-Boltzmann distribution, the temperature at which 2% of the atoms will be in the excited state is _____ K. (up to two decimal places)
(Boltzmann constant \(k_B = 8.62 \times 10^{-5}\) eV/K)
- IIT JAM PH - 2025
- Mechanics