# 18-2 - Example 1: A hollow aluminum cylinder 20 cm deep has...

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Unformatted text preview: Example 1: A hollow aluminum cylinder 20 cm deep has an internal capacity of 2 L at 20C. It is completely filled with turpentine and then slowly warmed to 80 C. (a) How much turpentine overflows? (b) If the cylinder is cooled back to 20C, how far below the cylinder's rim does the turpentine's surface recede? NOTE Ave. Coefficient of Linear Expansion for AI: a=2.4x 10-51C &amp;quot;' Ave. Coefficient of Volume Expansion for Turpentine: ~=9.0x 10-41C \:?.\, I~ ~ 1 . ~~m u .- 2. L .-~t\M\;I'\M~ E~lei---- ~ ~ 'I,fl.) \+C\A.I \l\A.tJc..L..- ~'i'~-h'~ C\lw+(&amp;quot;ws 1-- A V I&amp;gt;r\.= ~ /rl.. V,~ 6. T:: (.3oVlrl. V ~~T ~-= ~.:(Po.f '/./0- '3 L b~\j-r:-- ~T-V; ~r-~ ('1 )Cib-~ (- c.) C1-l.)~Q- G) ::::-O.tO'8L-- ~ t==iIl it J- ~J-ttA-V&amp;quot;y.a--Hv\c- &amp;lt;\$ 20 '&amp;quot; C-) ~ W ..,.,.. IML-J. +c---g D. c..- ~-'1l 3 (~~~)IO-S&amp;quot;' I-c..) (L. \-) (~o.~J T'-&amp;quot;e. AV\M/);'.~+~?:lIeJ 1s \J.()-T- \~..J.~':JI\L-= (ViT~Vr) ~ (v&amp;quot;+ ~Vlt~) ~AV~=~\!~t----::..6. to 3 t...- 0, C2-D'B &amp;quot;4 ....-:::: O'm lc.::LO~ \-- ~------------- ..-------- -- .~ t- _~_I~~A-J_.G:~s~~~--J:YlQ5+ ..+ ~_-1ftev.LYt~L~~C_. ~~~-'se~ _uJe-~flr-c/,'5';;-~\$S---':-_- ~e--'~~_~{~t2- ~-~------------- ------ - ..--- ..---------------- ~ ~ L- .!-.v'D~~-h&amp;gt;'l:mJ&amp;quot;)_- Ril &amp;quot;fl.te;rr--.CJ_~f-ItIVlYS----- ..----- ~Ave, _..Cl1.YYlprlC!.\$~b/e.-.~--- - - ;--+---- ;--..- '----~ _--:- -- -=-~-- ~~ ~_-&amp;gt;;M~I&amp;quot;) ~\oo,*~.e\$__~L;'(~-fy...~ ~'M'::~ ~Jd._~-1--&amp;gt;-+-~ _o_L~~-~O-+;~~-~{&amp;quot;'_~-PM*ide5:_~::r'!-~ Qcc.-u:rlj-ritl4:lI facile+!.-.&amp;quot;I *f~~;-4 N 1 ..1 1.L1 b.e L,-' .L I I--&amp;gt; '----~p1 _Olttj-yO\~~..!~\~vo-c,&amp;quot;n~~___~~-'j'MV vc.-e5- ?~'K~ vw.o-H~.--i ..------------.--~-------~------;--.- i-'~--- +-t------i--i ---- ;-+----- --..--- - - -- .-- ~--- ,--&amp;gt; t---- .-_.- I- --j-- f--------- ~---t ,-;-- n.---------- &amp;gt;---- - - ;-----+ j I-7If~t 'I~)-- ~- ~----\-p~ &amp;quot;&amp;quot;'-flit- -rf- --- -N , ::- -zt ~f&amp;quot;&amp;quot;'4.:~L(. . ~ ~ . C ~N~ I ~ ~ --- ..-..~~1.--- --- -f--- ------;--- j.g.- ~1j-~AI'\.4_~-~&amp;quot;&amp;quot;'~rtu4-tlt- &amp;gt;--! 1'13il'f-jQ_--,--t-~--+ I-f-E'&amp;amp;~.v.J_~~O\.L\) _We.--~-~- _..l4.(l~-L..Q.-~ kAw------------- I ~- ..-r~'J-i_~~J ~-- ~~ -~-?- t-[YAJ~_; ?r~~vv'e.----I-- - t ~&amp;gt;--~=-r-~----- ,-~:-- -- -- ..---- '..- \J 'h..v'V1:1= VQ }VVV1~..--- ~---- ------ V\-- --- ~ 0+ ~l_&amp;quot;} ~5----'- -- --- _B ~ \..t\.0i&amp;quot;~5&amp;quot;J j0\5~ ~&amp;quot;Vl5_~~T,_-,_8'...3l L{- &amp;gt;------------ ~-------- 1--- .. t--- \-h.~L~~t we. u~- ~!;??_---- --------------~- L ----------- t------ ~~~+- ~-C,,~~V-\C.~-)-- ~ V= '&amp;quot;' RT-~-- Ii ~c...J'-~ ~(/- lc_w~T g~~~ _l~ f.- ..- ~--+---~-- , .--- - --&amp;gt;----- ----- ,------ f----- -+----- ---i-- - ~-- ;-'---...............-- &amp;gt;----- ~.--- I t------ ,-------~- I Example 2: Imagine air in a cylinder initially at 20C supports a piston of mass 5 kg. The cylinder is lowered into a cooler until the temperature of the air in the cylinder is 5C. What is the ratio of the final to initial volumes?...
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## This note was uploaded on 04/20/2008 for the course PHYS 30320 taught by Professor Howk during the Spring '08 term at Notre Dame.

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18-2 - Example 1: A hollow aluminum cylinder 20 cm deep has...

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