Question

Problem 1 CH7/5pts Warm up. Show that: 1. PK 1- P ()where is the isothermal compressibility 2. PB 1+T (n)pwhere B is the thermal expansion. р' 3. Show that Te, Pe and Vm.e in a system described by a van der Waals equation of state depend only on a and b parameters.

Answer 1

Answers :

Problem 1

Q.1 and Q.2

Question No. i From he defimation of ibotherma compressibiliy Fac r, we kno that, iso thermo! compres sibilihy Foc tor (k) is de fimed Molosvolume oas Chonge of volume ea pessne (p) ot constant temp (T) T (Sgn in dicates the compre ssi on. deviation foctun NoLa Hhe compre ssion foc tor for real gas hen P.Vm R- miver sal ah constant RT AT No, diferentialing both side oih respect o coms tant temp (T), at

T Ym T ap R and T one coms Fant P T P T (pTved we have fo Questhom No Frm the defim tiom of ther mol expom siom-, thermal espansion co-tfficient is defmed VMT P- Thermal espansion co-efficient VinMolar vlu me of s

Change im volume 4ih res pect temp. (T at cons tamt pressurefp) to Novo RT toking hatora! differen tiating bth side with vespect to temp r) at eonstant pre ssre conditiom, -() 0 m 1 om 2T Proved) N8. there is prinlimg mistak e in the. uestiom

Q. 3

Critical Temperature (T_c​​​​​​) :  It is the maximum temperature at which a gas can be liquefied i.e. the temperature above which a liquid can not exist.

Critical pressure ( P_c) : It is the minimum pressure required to cause liquefaction at the temperature T_c.

Critical molar volume ( V_{c, m} ) : It is the volume occupied by one mole of a gas at critical temperature, T_c, and critical pressure, P_c.

We have to prove that P_c, T_c and V_{c, m}   only depends on Van der waal's constant a and b .

Van der waal eua tiom as- Pt a RT For mal P Presswre of fhe gas VmMoje vojume a,b Yan der waal cons Fan/- T Tempera ture RT Vm- b P+ RT V VIm-b a RT T (5 (v-) T A eneal paint ie. when T Te and V= Ve then dp T an d 0

There fore R Te () RT К? Vnib ond Ca ART (Vmyrb)3 /m2 Ca Vme (7) (Vb Vme Noua Dividing (6) ) (vae-b) Ga -b 3 3 b 3 Vm M,C 3 b ubstitebing in (6 R Ta (36) (3 b-b)

R Tc ,Tc dRb 50, rom Q R Tc (Vmc a7Rb (36-) X 4a Pe a 96 4a-3a Pc = 30 From eqt atíom 8 9 am d 10 i is proved that P Ve and Te o^ depe nds van der cwaal con stant C Proved) a,b

(Answered)