80 Official GATE PH Questions with Verified Solutions & Answer Keys
The partition function of a single gas molecule is Z. . The partition function of N such non-interacting gas molecules is then given by (A) (B) (za)" (C) N(Za) (D) (Z....
A heat pump working on the Carnot cycle maintains the inside temperature of a house at 22° C by supplying 450 kJ s'. If the outside temperature is 0° C, the heat taken, in ', from ...
The vapour pressure p (in mm of Hg) of a solid, at temperature T, is expressed by In p = 23 -3863/T and that of its liquid phase by In p = 19 -3063/T . The triple point (in Kelvin)...
The free energy for a photon gas is given by F = VT', where a is a constant. The entropy S and the pressure P of the photon gas are (A)S = 4 3 -aVT, P== 3 -T" (B) S= 3 -aVT', P= 4a...
Variation of electrical resistivity p with temperature T of three solids is sketched (on and R. different scales) in the figure, as curves P, Q Which one of the following statement...
Thermodynamic variables of a system can be volume V, pressure P, temperature T, number of particles N, internal energy E and chemical potential j, etc. For a system to be specified...
The pressure versus temperature diagram of a given system at certain low temperature range is found to be parallel to the temperature axis in the liquid-to-solid transition region....
The plot of inverse magnetic susceptibility 1/x versus temperature T of an antiferromagnetic sample corresponds to (A) (B) 1/x 1/x Tc Tc 0 T (C) (D) 1/x 1/x 0 Tc Tc T...
A common emitter transistor amplifier circuit is operated under a fixed bias. In this circuit, the operating point (A) remains fixed with an increase in temperature. (B) moves towa...
Two identical particles have to be distributed among three energy levels. Let rg, Ip and re represent the ratios of probability of finding two particles to that of finding one part...
A photon gas is at thermal equilibrium at temperature T. The mean number of photons in an energy state & = ho is...
Consider a system of N atoms of an ideal gas of type A at temperature T and volume V. It is kept in diffusive contact with another system of N atoms of another ideal gas of type B ...
The lattice specific heat C of a crystalline solid can be obtained using the Dulong Petit model, Einstein model and Debye model. At low temperature hw >> kT, which one of the follo...
An intrinsic semiconductor with mass of a hole m,and mass of an electron m, is at a finite temperature T. If the top of the valence band energy is E, and the bottom of the conducti...
The dependence of the magnetic susceptibility (X) of a material with temperature (T) can be represented by X oc T- 0, where ® is the Curie-Weiss temperature. The plot of magnetic s...
The dependence of the magnetic susceptibility (X) of a material with temperature (T) can be represented by X oc ,, where 0 is the Curie-Weiss temperature. The plot of magnetic susc...
The de Broglie wavelength of particles of mass m with average momentum p at a temperature T in three dimensions is given by (A) 2 = (B) 2= (C) 2= (D) 2=- h J2mk,T J3mk,T V2k,T J3m...
For a Fermi gas of N particles in three dimensions at T = 0 K, the Fermi energy, Ef is proportional to (A) N2/3 (B) N3/2 (C) (D) Nº 11/16 2009 PH...
The Helmholtz free energy of the system is given by (A) -KgTln(1+e &/kBT) (B) kgTIn(1+e6/kgT) (D) E-kgT (о) -к,T...
The specific heat of the system is given by e E/kgl e-elkgT (A) KgT (1+e-e/kT)3 KgTa (Ite-olkst) (C) se-ElkgT (D) e-E/kgT (1+e-81KgT)} KgT' (1+e-8/kgT)} Common Data for Questions 5...
The spectrum of radiation emitted by a black body at a temperature 1000 K peaks in the (A) Visible range of frequencies (B) Infrared range of frequencies (C) Ultraviolet range of f...
Wincip of the following atoms cunnol exhibit Bose Einsicin condenstion, even in (1)'Il, (В) "Не, (C) "Na,, (D) "K,o PH 3024 2010 "H...
CO, molecule has the first few energy levels uniformly separated by approximately 2.5 meV. Al a temperature of 300 K, the ratio of the number of molecules in the 4'"' excited slate...
The specific heat of the photon gas varies with temperalure as (A) (B) Cy cv T* (C) (D) T T...
For an intrinsic semiconductor, m, and m" are respectively the effective masses of electrons and holes near the corresponding band edges. At a finite temperature, the position of t...
A system of N non-interacting and distinguishable particles of spin 1 is in thermodynamic equilibrium. The entropy of the system is (A) 2kg In N (B) 3kg In N (C) Nkg In 2 (D) Nkg I...
A system has two energy levels with energies & and 2E. The lower level is 4-fold degenerate while the upper level is doubly degenerate. If there are N non-interacting classical par...
A classical gas of molecules, each of mass m, is in thermal equilibrium at the absolute temperature, T. The velocity components of the molecules along the Cartesian axes are , x y ...
Identify the CORRECT energy band diagram for Silicon doped with Arsenic. Here CB, VB, ED and EF are conduction band, valence band, impurity level and Fermi level, respectively....
The total energy, E of an ideal non-relativistic Fermi gas in three dimensions is given by 53 23 N E V where N is the number of particles and V is the volume of the gas. Identify...
Inverse susceptibility (1/) as a function of temperature, T for a material undergoing paramagnetic to ferromagnetic transition is given in the figure, where O is the origin. The v...
A simple cubic crystal with lattice parameter ac undergoes transition into a tetragonal structure with lattice parameters at = bt = 2 ac and ct = 2ac, below a certain temperature. ...
Consider a system whose three energy levels are given by 0, and 2. The energy level is two-fold degenerate and the other two are non-degenerate. The partition function of the ...
An n-channel junction field effect transistor has 5mA source to drain current at shorted gate (IDSS) and 5V pinch off voltage (VP). Calculate the drain current in mA for a gate-sou...
There are four energy levels E, 2E, 3E and 4E (where E > 0). The canonical partition function of two identical fermions is (A) e^(-5βE) (1 + e^(-βE) + e^(-2βE) + e^(-3βE) + e^(-4βE...
There are four energy levels E, 2E, 3E and 4E (where E > 0). The canonical partition function of two distinguishable particles is (A) e^(-5βE) (e^(2βE) + e^(βE) + 2 + e^(-βE) + e^(...
Which one of the following is a fermion? (A) α particle (B) 4Be7 nucleus (C) Hydrogen atom (D) Deuteron...
The plot of specific heat versus temperature across the superconducting transition temperature (𝑇𝑇𝐶𝐶 ) is most appropriately represented by (A) (B) (C) (D)...
The donor concentration in a sample of n -type silicon is increased by a factor of 100. The shift in the position of the Fermi level at 300K, assuming the sample to be non degenera...
For a system of two bosons, each of which can occupy any of the two energy levels 0 and ε, the mean energy of the system at a temperature T with T kB 1=β is given by (A) βεβε βεβε ...
The emission wavelength for the transition 1D2 → 1F3 is 3122 Å. The ratio of populations of the final to the initial states at a temperature 5000 K is (ℎ = 6.626 × 10−34 𝐽𝐽. 𝑠𝑠...
Consider a system of 3 fermions, which can occupy any of the 4 available energy states with equal probability. The entropy of the system is (A) 𝑘𝑘𝐵𝐵ln2 (B) 2𝑘𝑘𝐵𝐵ln2 (C) 2𝑘...
Given that the Fermi energy of gold is 5.54 eV, the number density of electrons × 1028 m-3 (upto one decimal place) (Mass of electron = 9.11 × 10-31 kg; h = 6.626 × 10-34].s; 1 eV ...
The band gap of an intrinsic semiconductor is E, = 0.72 eV and my = 6m*. At 300 K, the Fermi level with respect to the edge of the valence band (in eV) is at (upto three decimal pl...
The average energy U of a one dimensional quantum oscillator of frequency @ and in contact with a heat bath at temperature T is given by (B) U=-rosinh ¿Bro) (0) U=natanh - Bro...
The total power emitted by a spherical black body of radius R at a temperature T is P,. Let P, be the total power emitted by another spherical black body of radius R/2 kept at temp...
The entropy S of a system of N spins, which may align either in the upward or in the downward direction, is given by S = -k,N[pln p +(I- p)In(1- p)]. Here ke is the Boltzmann const...
N atoms of an ideal gas are enclosed in a container of volume V. The volume of the container is changed to 4V, while keeping the total energy constant. The change in the entropy of...
C'onsider a metal which obeys the Sommerfeld model exactly. If Er is the Fermi energy of the metal at T= 0 K and Rg is its Hall coefficient, which of the following statements is co...
The number density of electrons in the conduction band of a semiconductor at a given temperature is2x10' m 3 . Upon lightly doping this semiconductor with donor impurities, the num...
A solid material is found to have a temperature independent magnetic susceptibility, x = C. Which of the following statements is correct? (A) If C is positive, the material is a di...
The Fermi energies of two metals X and Y are 5 eV and 7 eV and their Debye temperatures are 170 K and 340 K, respectively. The molar specific heats of these metals at constant volu...
A two-level system has energies zero and E . The level with zero energy is non-degenerate, while the level with energy E is triply degenerate. The mean energy of a classical partic...
(C) 20o (D) 4 Correct: 1 Wrong: -0.33 Consider a triatomic molecule of the shape shown in the figure below in three dimensions. The heat capacity of this molecule at high temperatu...
A reversible Carnot engine is operated between temperatures I, and I, (I, > [,) with a photon gas as the working substance. The efficiency of the engine is (A) 1-- 4T2 (B) 1- T, 2 ...
Water freezes at 0° C at atmospheric pressure (1.01x105 Pa). The densities of water and ice at this temperature and pressure are 1000 kg/m and 934 kg/m' respectively. The latent he...
Consider a 2-dimensional electron gas with a density of 1019 m?. The Fermi energy of the system 1S _ eV (up to two decimal places). (m. =9.31x10-31 kg, h = 6.626x10-34Js, e = 1.602...
Consider N non-interacting, distinguishable particles in a two-level system at temperature T. The energies of the levels are 0 and &, where & > 0. In the high temperature limit (kg...
The energy density and pressure of a photon gas are given by u = aT* and P=u/ 3, where T is the temperature and a is the radiation constant. The entropy per unit volume is given by...
At low temperatures (T), the specific heat of common metals is described by (with a and B as constants) (A) aT + BT3 (B) BT3 (С) еxр(-а/T) (D) aT +BTS...
The high temperature magnetic susceptibility of solids having ions with magnetic moments can be described by x oc * with T as absolute temperature and as constant. The three behavi...
Amongst electrical resistivity (p), thermal conductivity (k), specific heat (C), Young's modulus (Y), and magnetic susceptibility (X), which quantities show a sharp change at the s...
Inside a large nucleus, a nucleon with mass 939 MeVcª has Fermi momentum 1.40 fm 'at absolute zero temperature. Its velocity is Xc, where the value of X is (up to two decimal place...
A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy e state. Both states are non-degenerate. If the total energy of this ensemble is 4e...
An air-conditioner maintains the room temperature at 27 °C while the outside temperature is 47 °C. The heat conducted through the walls of the room from outside to inside due to te...
Two solid spheres A and B have same emissivity. The radius of A is four times the radius of B, and temperature of A is twice the temperature of B. The ratio of the rate of heat rad...
The partition function of an ensemble at a temperature T is 2=(2cosh 7)" . where kg is the Boltzmann constant. The heat capacity of this ensemble at T = = is X Nks, where the value...
The quantum effects in an ideal gas become important below a certain temperature Ta hen de Broglie wavelength corresponding to the root mean square thermal speer ecomes equal to th...
In order to estimate the specific heat of phonons, the appropriate method to apply would be (a) Einstein model for acoustic phonons and Debye model for optical phonons (b) Einstein...
At temperature T Kelvin ( ) K , the value of the Fermi function at an energy 0.5eV above the Fermi energy is 0.01. Then T , to the nearest integer, is __________ ( 5 8.62 10 / B k ...
In a thermally insulated container, 0.01 kg of ice at 273 K is mixed with 0.1 kg of water at 300 K . Neglecting the specific heat of the container, the change in the entropy of the...
Consider two system A and B each having two distinguishable particles. In both the systems, each particle can exist in states with energies 0,1,2 and 3 units with equal probability...
As shown in the figure, an ideal gas is confined to chamber A of an insulated container, with vacuum in chamber B. When the plug in the wall separating the chambers A and B is remo...
According to the Fermi gas model of the nucleus, the nucleons move in a spherical volume of radius R (= R, 4?, where A is the mass number and R, is an empirical constant with the d...
(A) (B) The internal energy U of a system is given by U(S,V) = 2V-2/3g2 , where 2 is a constant of appropriate dimensions; V and S denote the volume and entropy, respectively. Whic...
To sustain lasing action in a three-level laser as shown in the figure, necessary conditions) is(are) 2 (A) lifetime of the energy level 1 should be greater than that of energy lev...
As shown in the figure, inverse magnetic susceptibility (1/x) is plotted as a function of temperature (T) for three different materials in paramagnetic states. %. T (Curie temperat...
The canonical partition function of an ideal gas is Q(T, V, N) = 1 N! [ V (𝜆(T))3] N where T, V, N and 𝜆(T) denote temperature, volume, number of particles, and thermal de Brogli...
Consider one mole of a monovalent metal at absolute zero temperature, obeying the free electron model. Its Fermi energy is EF. The energy corresponding to the filling of NA 2 elect...
Consider a two -level system with energy states +𝜀 and - 𝜀. The number of particles at +𝜀 level is N+ and the number of particles at - 𝜀 level is N-. The total energy of the sy...