7/26/2019 PH2103 AY1314 Midterm-Exam

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NANYANG TECHNOLOGICAL UNIVERSITY

MIDTERM EXAMINATION 2013-2014

PAP 213 !"#$%&' )"*+,-+

Oct 7th Time Allowed: 2 Hours

INSTRUCTIONS TO CANDIDATES

1.This examination paper contains Four (4) questions and comprises THREE (3)

pages, including this page. There is a bonus question that is worth 0 mark.

DO NOT ATTEMPT THIS QUESTIONUNLESS YOU HAVE FINISHED

ALL OTHER QUESTIONS

2.

Answer ALL FOUR (4) questions.

3.Answer each question beginning on a FRESH page of the answer book.

4.This IS NOT an OPEN BOOK exam.

5.One A4 size cheat sheet with written notes on one side is allowed.

6.Candidates may use calculators. However, they should write down systematically

the steps in the workings.

7.The book of physical constants is provided for reference only. Do NOT make any

marking on it and do NOT remove it from the examination hall.

7/26/2019 PH2103 AY1314 Midterm-Exam

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1. The first law of thermodynamics is usually written as !U = Q + W.

(a) Define each of the terms !U, W and Q and briefly explain the meaning and

significance of the first law.(b) In a few sentences, clearly explain the differences between temperature, heat

and internal energy.

(c) Briefly discuss how compressive work in a gas is given by the expression

W ! #$ PdV .(d) 1 L of air at 1 atm and 298 K is expanded isothermally to a pressure of 0.5 atm.

Calculate the work done in this process and comment on the meaning of the sign

of the result.

(25 marks)

2. One mole of isolated ideal monoatomic gas undergoes transformation from the

initial state for which pressure and volume are 8 atm and 5 liters, respectively, to a

final state where the pressure and volume are 4 atm and 15 liters, respectively.

(a)

Calculate the change in internal energy of the ideal gas

(b)During the transformation process, the pressure and the ideal gas has quadratic

relationship P = aV2

+ b. Calculate the constants a and b. Also, calculate thework performed and the heat absorbed by the ideal gas

(c)Write down the temperature of the ideal gas as a function of the volumeduring in the processes in (b)

(25 marks)

3. Consider a system in which the particles are Thermal Physics students (114

students) confined to room TR3 (150 seats). Suppose the particles have no kinetic

energy so they occupy chairs in the room and there is no interaction energy so

there is at most one particle per chair. What is the entropy of the system?

(25 marks)

4. Suppose the multiplicity function of a system is given by:

What is the heat capacity (constant volume) of this system? Hint: First, find the

entropy, then the temperature as a function of the internal energy, then use it to find

heat capacity

(25 marks)

7/26/2019 PH2103 AY1314 Midterm-Exam

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****Bonus Question**** (warning attempt this question only after you have

finished the 1st4)

There is a 1-D chain consisting of n (>>1) elements as seen in the figure. Let thelength of each element be a and the distance between the end points x. Find theentropy of this chain as a function of x and obtain the relation between the

temperature Tof the chain and the force (tension) which is necessary to maintain thedistance x, assuming the joints to turn freely.

****(0 mark)****