A Concise Introduction to Thermodynamics For Physicists Patrcia Fasca

A Concise Introduction to Thermodynamics For PhysicistsPatrícia Faísca Chapter 1 - Thermodynamics Key Concepts Problem 1.3 Use the ideal gas pressure equation of state to determine the densityflof an ideal gas at standard atmospheric temperature (T= 20 ¶

• and pressure (P=1atm).

Problem 1.4 The mean radius of an air molecule (O 2or N2) is 0.15 nm. The average distance between near- est neighbour particles in the gas is3.5◊10 ≠9 m at standard atmospheric pressure and room temperature. Can the air be modelled as an ideal gas?Problem 1.5 Consider the isothermal, isobaric and isochoric processes of the ideal gas represented in Figure 1.Determine the order (from smaller to larger) betweenT 1,T2andT 3,P1,P2andP 3, andV 1,V2 andV 3.Figure 1 Problem 1.6 A closed cylinder has a freely moving diathermal piston separating two chambers of lengthsL 1 andL 2. Chamber1contains25mg of N2, while chamber 2 contains40mg of helium gas. In thermodynamic equilibrium, what is the ratioL 2/L1? And the ratio between the number of moles of N 2, to the number of moles of He?Problem 1.7 Estimate the number of molecules in an isothermal atmosphere as a function of height.Hint: Model the atmosphere as an ideal gas and consider a molecule at temperatureTsubjected to gravity.Problem 1.8 A vertical right cylinder oh heighth= 30cm and base areaA= 12cm 2 is sitting open under standard atmospheric temperature and pressure. A5.0kg piston is placed into the cylinder and allowed to move without friction to a final equilibrium position. Assuming the final temperature to beT=0 ¶ C, what is the equilibrium height and pressure?Problem 1.9 From a thermodynamics standpoint, what is the di!erence between ahotbaseball at rest and a coldbaseball moving at high speed?Problem 1.10 Consider a sphere of radiusRand volumeV. Show that when expressed as a function ofV,R 3 (V) is an homogeneous function of degree one.1 p VT Solutions Manual for A Concise Introduction to Thermodynamics for Physicists, 1e by Patricia Faisca (All Chapters) 1 / 4

Problem 1.11 Classify the following processes as reversible, irreversible or quasi-static.

a) Squeezing a plastic bottle.

b) Ice melting in a glass of hot water.

c) Pumping air into a tyre.

d) Compressing a gas with a real piston (i.e. with friction).

Problem 1.12 The Celsius temperature scale is defined by setting the freezing point of water equal toTf=0 ¶ C and the boiling point of water equal toT= 100 ¶

• On the other hand, the Kelvin (or absolute)

temperature scale is defined by setting the freezing point of water equal toTf= 273.15K and the boiling point of water equal toT= 373.25K. Determine the relation between the two temperature scales, i.e., show thatT(K)=T( ¶

C) + 273.15

Problem 1.13 Consider the Maxwell-Boltzmann distribution. Evaluatevp.Problem 1.14 Use a software of your choice to evaluate the Maxwell-Boltzmann distribution of the following

gases atT= 273K: O2,N2, He, H2,H2O. What do you conclude?

Problem 1.15 Starting from the Maxwell-Boltzmann distribution, determinef(EK)dEK, i.e., the fraction of gas particles with kinetic energy betweenEKandEK+dEK Problem 1.16 Evaluate the fraction of oxygen molecules with199

• atT= 27

¶ C.Problem 1.17 In a gas, which fraction of particles havevvrms?Problem 1.18 Derive an expression of the number of collisions between the particles of an ideal gas and a planar surface of areaA, during time interval!t, by unit area and unit time. Express your answer as a function of the gas pressureP Problem 1.19 A solid surface with dimensions2.5nm by3.0nm is exposed to gaseous argon atT= 500K and P= 90Pa. How many collisions occur with the surface during15seconds?

2 2 / 4

SOLUTIONS

rm = wyi 'T 4.30 * \a 3 x2-^ 3 = 2r&xto 2-3 C ^ rVdUjJ' MA 3 =h\,C,yJlfnu.^

N=—WJ K

^ T P ^ =WtcBT <- ?> = -e PTs ~ l - £r>=0-lS " ^ AM <- i> s3-rvio-^AM-— 3- S ' - 2d_ WWGIA.'YNAAOASt's O ^ JfiT ^ ^ r> IM* ^ I '- ( V ^ r-K* KtHAA (4k?rwr?f«L‘?/+W.^Vi'4 ^-ftf-MJL& [flo fgS 'Wv ^ ljCP'Vurjaer“H<«_ e ^ Jif *y.slori ^ s-f- 'di' ^ levv ^ tW4W-6MA-K * CJ.IAlot\J.4\iJed- toc/w i'«Lea( at * -fw ^ £ .\1»cIPV=NK 8T

jTsa{Wvuu * .|( ^ V »

'5c&uaWk-):T\>^

2/> " ^ 3 iCsalo.** >’« ^ Pisc ^ s-lsw-V ^ i

jCsacUflCi' ^ (VI- SC* >UsWvt\-J

:

§ywvP 3> ^ > p 1 prr (£)“*«, > V 1 V-

H 3 / 4

un Ik.VI 2_ JL 2_ 2.“?<7\A.£ _ ^towg- f- I=fa.- P T- j=

*T—^^

>fs4oV\ L| TVus / PV!=RTCi; PV 2.= / wL R-rca.; _ CO_ /rSV\ ^ C- 'k) Viz_

/VL-—

lMo&cvwM4 - <6 * T"X\D < ^ >J ^ L= 2- g V\ Q ~ '

• _

0- 8< !_ 0.00 ^AoX16 £ kvlo-'3 V2.\o TliOAd2- Q fw'rh*- h/lV\

Jj ^ Q.<= W * f- ^ fcf .-tw t Cyw * .^ + \A/aY'iXs ^ Of ( <2_ JLXgfkdL-I '/' tMXjw- beWw,wI-VV.^ ptv) 4wjscdj' fi * .a-lW ^ jUb-fcEH

• / 4