Quiz7_Solution

Quiz7_Solution - Quiz 7. Monday, March 24‘“, 2008 PHY...

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Unformatted text preview: Quiz 7. Monday, March 24‘“, 2008 PHY 252 Name. SOLu—nozu 1. Two blocks of copper, each exactly of 1 kg mass, are placed in a well- insulated container so that no heat can flow in or out of the system (:12. Bl°°k l BIOCI‘ 2 it is a closed system). Block 1 is initially at temperature Tl =60.0 °C, block 2 is initially at temperature T2 = 20.0 °C. Cu Cu 1.0 kg 1.0 kg (a) Calculate the equilibrium temperature Tf. (1 point) 600 DC 200 0C From lsi: law Qt°t=o = Q‘+Qz QI+ at. = MIC-i (T; -T;) + MIC1CTg-T;) ‘-‘-‘ O :2) T3, = “‘31; IMICITI -.-_-_ éCTl-iT-g) = 41(60‘c.+2.o°c) 2' 40°C — 'A‘ (b) Calculate the change in e‘ii‘ti’cffiy of the system, ASJr once equilibrium is reached. (CCll =390J/kgoK) (1 point) Téd Tédfl T 1" ASed» ='- A5. + A5,. = J .3: + 3 __.=== mgj‘il: +M1ctj‘fl’ "r. T 1.‘ T T 'T‘ T T ‘ I. Astot = nigh-1%- +“:Ca1H-Ii 7:. “cauLAI—E ‘ Ta, TIT}, 1. as“ = (1:3)(aaomna.n)u[_&_m_ -.-. l-é'J'IK *- (z‘i‘SHCSBI) (c) Now consider the system before equilibrium is reached. After some time a certain amount of heat Q is transferred from block 1 to block 2. The temperature of block 1 has fallen by an amount AT , and the temperature of block 2 has risen by an equal amount AT (since they have the same mass and specific heat, and heat is conserved by the 1st law), but neither has yet reached Tf. Derive down an expression for the entropy change of the system AS in terms of AT , m, CONT“ and T2. (1 point) Frau lsi law Ql = - at ‘= -MCAT 11-51“ “Ru-r AS ::.- AS.+ASL == ‘73-! + 9L9.- :_ WICcu +1“ EAT) T‘ T T T T. 1-I I. ((1) Now solve for the value of AT that maximizes AS . (Hint, solve d(AT) = 0 ), and comment briefly on the physical insight revealed by your result. (2 points) Differentiate AS: dcas) :: urn—GEE. + lid—‘1‘. = a forum: orm‘u‘ cl CAT) Fr! "AT Tad-HAT ' % -TI+AT +T1+AT =0 ==> AT = 1"“ : 50°C“2°°‘ -..-. 206° '2- 2 “There is atumiufl Poiulr for AS when col-tickle T5 . To elect-J: ‘15- N.” is a. Maxi-mum or CLICAS) .__ ._ WIng “(6“ h.- atcm‘ ("n—ATP (mm: Eiuilibr‘fum CorrespauaLs to 'the. maximum eu‘Lropd change that? is canalsten‘t wit-L.__'l:ke "its!- low . =‘T.-AT = 60-10 = 40°C Mimmum 6! :Hereu'tliat'e ad q in < O alwaflL .‘. 4-5 .15 mxfiflflhd‘fi Quiz 7. Monday, March 24‘“, 2008 PHY 252 2. An ideal heat engine has a theoretical efficiency of 25.0 % when the high temperature reservoir is at TH = 127 °C . (a) What is the temperature of the low temperature reservoir, TL ? (1 point) e , .__= l __ “Tc. Ideal. 3F: 0.25. ___ l.._ -r¢_ a 1.. :5 @119: trooth—oar) 2?3N2?-K ‘HDOK Tc = 300 k .....__.. + In one cycle, a real engine extracts 250. J of heat from the hot reservoir while doing 40. J of work. (b) What is the actual efficiency of the engine? (1 point) ._. _. T ._.. ecu-114.4 ‘ 19/— —- “'0' = 0.14 :2 16% -— =14 Qu 2 s 0.3 (c) How much heat per cycle is exhausted to the cold reservoir? (1 point) [Q4 : [QH[_[w] = 230.2:— A—oq‘ = 210:: i4 3. 1.00 g of ice at 0.0 °C melts in a large lake of water whose temperature is very slightly above 0.0 °C. Estimate the entropy change of the ice? (LF = 333 J/ g) (2 points) AS"; '2 7-7 5"— ~= ..M_L_§ 56-:- a.“ pretend e T T .1. Ast'ce = C "005) “_(_33__3 We) :. 1.22 T/K 9(- 2? 3 K What is the entropy change of the ice—lake system? (1 bonus point) 'qu. tux—.th macaw from rum at 0°C, .‘. Aside :: -— :LF 2:. -- 1.7.2. T/K an Aswan = 45,-“ +AsMe := L22 -r.22 = OU/k* 1e. JUL» imam; Pro-mass L4 rem—AM. ...
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This note was uploaded on 05/11/2008 for the course PHY 252 taught by Professor Treacy during the Spring '08 term at ASU.

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Quiz7_Solution - Quiz 7. Monday, March 24‘“, 2008 PHY...

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