The table below presents pumpdown data for a cylindrical vacuum dhamber (dimensions given below), as recorded by the vacuum gauges. At t=0, the gate valve was opened and the chamber was pumped down from 100m Torr using a diffusion pump ('Pumpdotvn stage'). When the chamber pressure reached 4.8106 Torr, the gate valve was dosed to isolate the damber and the subsequent rise in pressure recorded ("Outgassing stage"). Chamber data: System temperature 300K, radius 25cm, height 60cm. Chamber pumping ditfusion pump speed 2400L/s, conductances: water buttle 1500L/s cold trap 800L/s gate valve 1900L/s, damber oritice/ flange 2100L/s. Assume the pressure P(t) obeys the general system equatione VdtdP=SetilP+Q0(t) where Q0(t) represents the time dependent outgassiag load. There are no other Q terms present, ie., we re assuming no real leaks, etc.) (a) ( 6 marks) Fint, suppose there is no outgassing. What is the time constant F (the time required for the pressure to drop by a factor of 1 ) for a "clean" pumpdown? The ditfucion pump, cooling baffle, cold trap, gate valve, and chamber onifice are connected in series. How long "should" it take to pamp down the chamber troen 100m Torr to 4.8106 Torr? (Compare this number to the actual data!) (b) (10 marks) A general experimental obvervation is that outganing syitems obey a power law of the form P(r) \& tn during pumpdown. Contirm this graphically, using data for which t to Tp, and obtain a value for n using a linear least-squares fit. (c) ( 9 marks) After the gate valve is dosed, what is the ditfesential equation satisfied by P(n) ? Assuming that Q0(t) varies little during the measurements taken in the outgaseing phase, use (eg.) graphical means to obtain an estimate for Q9 in watts (work out the unit comversion carefully) at the instant the gate valve was dosed. What is the outgasing per (nominal)