L A N C A S T E R U N I V E R S I T Y

2010 EXAMINATIONS

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.

PHYSICAL CONSTANTS

Planck’s constant h= 6.63 ×10−34 J s

¯h= 1.05 ×10−34 J s

Boltzmann’s constant kB= 1.38 ×10−23 J K−1

Mass of electron me= 9.11 ×10−31 kg

Mass of proton mp= 1.67 ×10−27 kg

Electronic charge e= 1.60 ×10−19 C

Speed of light c= 3.00 ×108m s−1

Avogadro’s number NA= 6.02 ×1023 mol−1

Permittivity of the vacuum ǫ0= 8.85 ×10−12 F m−1

Permeability of the vacuum µ0= 4π×10−7H m−1

Gravitational constant G= 6.67 ×10−11 N m2kg−2

Bohr magneton µB= 9.27 ×10−24 J T−1(or A m2)

Bohr radius a0= 5.29 ×10−11 m

Gas constant R= 8.31 J K−1mol−1

Acceleration due to gravity g= 9.81 m s−2

1 standard atmosphere = 1.01 ×105N m−2

Mass of Earth = 5.97 ×1024 kg

Radius of Earth = 6.38 ×106m

Density of iron = 7.6×103kg m−3

please turn over

1

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

diagram.

(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 n−nand 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]

2

##### Document information

Uploaded by:
sadashiv

Views: 1189

Downloads :
0

Address:
Physics

University:
Allahabad University

Subject:
Thermal Analysis

Upload date:
20/02/2013