Ideal Gas Model - Thermal Properties of Matter - Exam, Exams for Thermal Analysis. Allahabad University

Thermal Analysis

Description: This is the Exam of Thermal Properties of Matter which includes Thermodynamic Quantity, Einstein’s Theory, Ehrenfest Classification, Phase Transitions, Thermodynamic Potential, Clausius-Clapeyron Equation, Molar Volume of Solid etc. Key important points are: Ideal Gas Model, Laws of Thermodynamics, Van-Der-Waals Gas Model, Equipartition Theorem, Lambda Phase Transitions, Specific Heat of Paramagnetic Solids, Schottky Anomaly, Definitions of Entropy
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L A N C A S T E R U N I V E R S I T Y
Part II
PHYSICS - Paper 2.D
Candidates should answer all those sections identified with the modules for which
they are registered.
An indication of mark weighting is given by the numbers in square brackets following
each part.
Use a separate answer book for each section.
Planck’s constant h= 6.63 ×1034 J s
¯h= 1.05 ×1034 J s
Boltzmann’s constant kB= 1.38 ×1023 J K1
Mass of electron me= 9.11 ×1031 kg
Mass of proton mp= 1.67 ×1027 kg
Electronic charge e= 1.60 ×1019 C
Speed of light c= 3.00 ×108m s1
Avogadro’s number NA= 6.02 ×1023 mol1
Permittivity of the vacuum ǫ0= 8.85 ×1012 F m1
Permeability of the vacuum µ0= 4π×107H m1
Gravitational constant G= 6.67 ×1011 N m2kg2
Bohr magneton µB= 9.27 ×1024 J T1(or A m2)
Bohr radius a0= 5.29 ×1011 m
Gas constant R= 8.31 J K1mol1
Acceleration due to gravity g= 9.81 m s2
1 standard atmosphere = 1.01 ×105N m2
Mass of Earth = 5.97 ×1024 kg
Radius of Earth = 6.38 ×106m
Density of iron = 7.6×103kg m3
please turn over
Section A: Module 233: Thermal Properties of Matter
(The time allocated for this section is 80 minutes.
Candidates should answer question A1 and
either question A2 or question A3.)
Compulsory question:
A1. (a) State the First, Second and Third Laws of Thermodynamics. [8]
(b) (i) Describe the assumptions of the ideal gas model. Sketch a set of isotherms
for three temperatures, where T1> T2> T3, for an ideal gas on a P-V
(i) Describe the assumptions of the Van-der-Waals gas model. Sketch a similar
set of isotherms for the Van-der-Waals gas on a P-Vdiagram. Clearly
identify an isotherm corresponding to temperature below which the Van-
der-Waals gas could be liquified. [8]
(c) State the equipartition theorem. Using the equipartition theorem, calculate
the internal energy and heat capacity at room temperature for one mole of i)
a monoatomic gas and ii) a diatomic gas. [8]
(d) Explain the distinction between first order, second order and lambda phase
transitions. Illustrate your answer with examples (one for each transition) and
sketches showing how the specific heat varies with temperature. [8]
(e) The specific heat of paramagnetic solids show a Schottky anomaly at low tem-
perature. Describe briefly what is a Schottky anomaly and how it can be
explained in terms of the microscopic properties of the system. [8]
Answer one of the following two questions:
A2. (a) Give definitions of entropy in the i) thermodynamical and ii) statistical frame-
works. Explain how the irreversibility of a process is linked to entropy. [16]
(b) (i) Calculate the number of microstates for a 2-level system that consists of
N-elements assuming that the temperature of the system is such that the
probabilities of occupying both energy levels are equal. Using Stirling’s
approximation ln n!nln nnand the statistical framework, calculate
the entropy of the system. [14]
(ii) Calculate the entropy of the same system when only the lowest energy level
is occupied. Discuss the temperature of the system in this case. Explain
whether the system is least ordered in this case or in case (i), when both
levels are occupied equally. [10]
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