Statistical Mechanics and Thermodynamics

Question Paper 2011 June Batch
Statistical Mechanics and Thermodynamics
The question paper contain 3 parts
Part A contains 20 questions. Answer any 15 questions (Each question carries 2 marks)
Part B contain 20 questions and all are compulsory (Each question carries 3.5 marks)
Part C contains 25 questions. First 10 are compulsory and from remaining 15, answer any 10 questions (Each question carries 5 marks)
There will be negative marks @ 25% of each wrong answer.

Time : 3hrs
Marks: 200

PART A
For polyatomic gases such as hydrogen the corresponding Phase Space would be ------- dimensional.
3N
3Nf
2Nf
6N
On a (T -S)) diagram, i.e., temperature (T) entropy (S), the isothermals are ---
Parallel to S axis
Parallel to T axis
May have any orientation
Some parallel to T and some parallel to S axis
In a gas the expression for the average speed of the molecule is given by----
√(2kT/m)
√(3kT/m)
√(8kT/πm)
√(kT/m)
Specific heats of a gas at constant volume (Cv) and at constant pressure (Cp) are related as
C_p/C_v =1-R
C_p-C_v=R
C_p-C_v=1/R
C_p+C_v=R
The expression for Maxwell’s distribution of velocities, δn/δc is
4πn (m/2πkT)^(3⁄2) e^(-(mc^2)/2kT) c
4πn (m/2πkT)^(3⁄2) e^(-(mc^2)/2kT) c^2
4πn (m/πkT)^(3⁄2) e^(-(mc^2)/2kT) c^2
4πn (m/2πkT)^(3⁄2) e^(-mc/2kT) c^2
A reversible heat engine can have 100% efficiency if the temperature of sink is-
Less than that of source
Equal to that of source
0oC
O K
In a gas the relative magnitudes of the most probable speed (v_p), the average speed (v ̅)and the root mean square speed(〖 v〗_rms) of the molecule are related by an expression
√2:√(2/π):√3
√2:√(4/π):√3
√2:√(8/π):√3
√2:√(8/π):√6
The combined form of the first and second law of thermodynamics is given by-
TdS=dU+PdV
dQ=TdS+PdV
dU=TdS+dQ
TdS=dU-PdV
A system has N distinguishable particles. Each particle can occupy one of the two non-degenerate states with an energy difference of 0.1 ev. If the system is in thermal equilibrium at room temperature, the approximate fraction of particles in the higher energy state is
exp (-10)
exp (-4)
exp (-2)
Zero
The work done W during an isothermal process in which the gas expands from an initial volume V1 to a final volume V2 is given by
R(V_2-V_1)〖log〗_e (T_1/T_2)
R(T_2-T_1)〖log〗_e (V_1/V_2)
RT〖log〗_e (V_2/V_1)
RT〖log〗_e (V_1/V_2)
Consider the Fermi-dirac distribution function F(E) at room temperature (300 K) where E refers to energy. If Ef is the Fermi energy, which of the following is false?
F(E) is a step function
F(E_f) has a value of ½
States with E F(E) is large and tends to infinity as E decreases much below Ef.
The change in entropy is-
Positive in a reversible change
Negative in an irreversible change
Positive in an irreversible change
Negative in a reversible change
In a micro canonical ensemble, a system A of fixed volume is in contact with a large reservoir B. Then
A can change only energy with B
A can change only particles with B
A can exchange neither energy nor particles with B
A can exchange both energy and particles with B
If a system is in thermal equilibrium separately with B &C, then B and C are also in thermal equilibrium with each other. This statement is –
Zeroth law of T D
First law of T D
Second law of T D
Third law of T D
In a canonical ensemble, a system A of fixed volume is in contact with a large reservoir B. Then-
A can change only energy with B
A can change only particles with B
A can exchange neither energy nor particles with B
A can exchange both energy and particles with B
In a cyclic process-
Work done is zero
Work done by the system is equal to quantity of heat given to the system
Work done does not depend on the quantity of heat given to the system
The internal energy of the system increases
In a grand canonical ensemble, a system A of fixed volume is in contact with a large reservoir B. then-
A can change only energy with B
A can change only particles with B
A can exchange neither energy nor particles with B
A can exchange both energy and particles with B
The ratio of specific heat of a diatomic gas is-
1.66
1.33
1.40
1.52
In case of Bose- Einstein Condensation-
Number of particles increases in lower energy levels at low temperatures and high pressures
Number of particles decreases in lower energy levels at low temperatures and high pressures
Number of particles increases in lower energy levels at high temperatures and low pressures
Number of particles decreases in lower energy levels at high temperatures and low pressures
Which of the following is not Maxwell’s thermodynamic relation?
(∂S/∂V)_T=(∂P/∂T)_V
(∂S/∂P)_T=〖-(∂V/∂T)〗_P