Question

1 a) Explain why a real gas that expands is cooled. Why is this effect only obtained at temperatures below 40 K for helium?
b) Calculate the mean path and root mean square velocity of helium atoms at 101.3 kPa and 40 K.
c) How would the medium path be affected for a gas trapped in a steel cylinder if heated?

Answer 1

Now, Root meen Square Velocity. Vemy me atomic mass = 4.003 mer = 4:003x10 Vorms EV3RT Why real gas expand outer ce gets cooled ? As a real gas get expand it's Volume increases. The frequency of atomic Collisions decreases as it's volume Intreases. So because of decrease in collisions, temperature gets decreased. Gases are a phase of matter where all the atoms moving Independently of each other all the times. Allmuletules muring toith different speed and average speed of all molecules yet temperatur, in expansion this speed derecase due to dem code in Collisio se 11) temperatung also demcase Cie enery needed to increase system temperature is taken by hum Syskem itself 6 temperbune deceases ) Voms : 348314 x 40 V 4:003163 - 499.23 m/s Noms : 499.23 M/S C > As we knowol le Joule - Them sun coefficient is always positive art very tous tempoetune and a boys negative at high temperatures, This explain the inveesion temperatue of each gos. In case of helium at temperature above hok the predominant interaction is repulsive. At this stote the gas stoet to expend. felhen it expand. energy is obtained as the molecule qe separate. Separation of molecule increases internal energy of hetim and it Sheet to get healed. How would the medium path affected for a gos trapped in sheet Cylinde if heated? As temperature of Minder increases, the gou molecules inside cylindee gain energy and their kinetic energy intreases which fun thing interesses the number of collision With these collisions peldne inide the ve cylinder intense. Headed gas then find path to flad out from cylinder as if the cylinder is closed, 9o, inince it's trinchic enreye calisima and also presiun intense). evetpesuwahion can cause domose to the finder so to reduce that dumaye, Safety valves are connected which sehe pean when it increase beyond extelin design petune of veel mean free path = t. K = Boltamenn Constanta T: Temperature -401 KT 7Up T: atomic redius PPrenuse = 101.3 kPa helium, amit radius 140 pm ie 146 Pecomelery kolo and ko po 3.3168 .138 x1623 6.072 1023 1-39x1623.40 unxvi (1404162) x (101300) F = 1.564x109 m