SPECIFIC HEAT AND HEAT OF FUSION

Transcription

1 PURPOSE This laboratory consists of to sparat xprimnts. Th purpos of th first xprimnt is to masur th spcific hat of to solids, coppr and rock, ith a tchniqu knon as th mthod of mixturs. Th purpos of th scond xprimnt is to masur th hat of fusion of ic. SPECIFIC HEAT OF SOLIDS Th spcific hat of a substanc is dfind as th hat nrgy pr unit mass that is rquird to chang th tmpratur of th substanc by on dgr (s your txt). It is usually givn th symbol c. Th unit of 'c' usd in th laboratory is Cal g -1 C -1. In gnral, th spcific hat of a substanc dpnds on its tmpratur. Th graph Figur 1 shos th tmpratur dpndnc of th spcific hat (in J K kg -1 K -1 ) of zinc. Most solids, including th ons ill b using, hav a similar tmpratur dpndnc. Not that nar room tmpratur (say 293 K) th spcific hat is a sloly varying function of tmpratur, and so in this nighborhood (ithin ± 25 K) th spcific hat is narly constant. In this xprimnt shall nglct th small variations in th spcific hat ith tmpratur and trat all spcific hats as constants. Th apparatus usd to masur spcific hats is a calorimtr as shon in Figur 2. It consists of to aluminum cups and a lid ith a hol providd for a thrmomtr. Th smallr of th to cups can b suspndd ithin th othr cup by mans of an "O-ring" mad of an insulating matrial. Th xprimnt is carrid out by th mthod of mixturs. A knon mass of atr at room tmpratur is addd to th innr cup. Th amount of atr must b such that it compltly immrss th sampl, hos spcific hat is to b masurd. Th sampl is placd ithin a boiling atr bath so as to rach th boiling tmpratur of atr. It is thn quickly transfrrd to th innr cup and th lid is placd on th calorimtr. Th mixtur is gntly stirrd until th final quilibrium tmpratur is rachd. VII-1

2 Th tmpratur is monitord ith a thrmomtr until th systm rachs its highst stabl tmpratur (thrmal quilibrium). In ordr to dtrmin th spcific hat of th sampl xprimntally, must mak som physical assumptions. Th calorimtr is spcifically dsignd to limit hat losss to th nvironmnt. It is thn natural to assum that no hat nrgy is transfrrd to th surroundings. This assumption allos us to considr nrgy transfrs that occur only btn th sampl, th atr, and th calorimtr. W should xamin th conditions undr hich this assumption is rasonabl. W kno that th calorimtr must lak som nrgy to th surroundings, for if r to ait long nough, th ntir systm ould rach room tmpratur. Th amount of nrgy transfr to th surroundings dpnds critically on th tmpratur diffrnc btn th systm and th surroundings. Thr ar thr ays hat nrgy can scap from th systm. Ths ar convction, conduction, and thrmal radiation. An isolatd systm, by dfinition, is immun to all thr typs of nrgy transfr. Hat transfr by convction rlis on convction currnts hich physically carry matrial (in this cas air) from on rgion to anothr. Sinc th calorimtr is covrd ith a lid, hat transfr du to convction can b minimizd and hnc it is nglctd. Th layr of air btn th innr and outr cups provids thrmal insulation for minimizing conduction. Th polishd aluminum cups ar intndd to provid mirror-lik boundaris to rflct thrmal radiation back into th systm, rducing th radiation losss. Th radiation ffct can also b minimizd by starting th original tmpratur of th mixtur as far blo room tmpratur as th final quilibrium tmpratur is abov room tmpratur. For th substancs involvd in this xprimnt and initially hatd to th tmpratur of boiling atr, a good stimat for th initial tmpratur of calorimtr and atr is about 10 C (this may vary) blo th room tmpratur sinc, th final quilibrium tmpratur is xpctd to b about 10 C abov th room tmpratur. Th choic of such an initial tmpratur ill rduc th radiation loss to ngligibl lvls although not compltly liminat it. VII-2

3 Th variabls ar dfind as follos. T i = initial tmpratur of th atr and calorimtr (innr cup + stirrr) - (approximatly 10 C blo room tmpratur) T s = initial tmpratur of th sampl (approximatly 100 C) T = quilibrium tmpratur of th sampl, atr, and calorimtr m = mass of atr in g m c = mass of calorimtr (innr cup + stirrr ) in g m s = mass of sampl in g c = spcific hat of atr = 1 Cal g -1 C -1 c Al = spcific hat of aluminum = Cal g -1 C -1 c = unknon spcific hat of sampl With th abov assumption can quat th hat nrgy gaind by th atr and th calorimtr ith th hat nrgy lost by th sampl. If solv th rsulting xprssion for th spcific hat of th sampl find, ( m c + m cc Al )( T Ti ) m ( T T ) c = (1) s s Th nrgy transfr to th thrmomtr is ignord in th abov analysis, vn though th action of th thrmomtr itslf implis that such an nrgy transfr xists. Th thrmomtr prsnts a problm bcaus part of it is intracting dirctly ith th systm hil th rst is compltly outsid of th systm. Thr ar (slightly complicatd) ays to includ th ffct of th thrmomtr but shall not pursu thm hr. W can, hovr, account qualitativly for th prsnc of th thrmomtr and othr nrgy losss in th sns that can dtrmin th dirction th spcific hat of th sampl ould b shiftd if r to includ thir ffcts. Our laboratory thrmomtrs can masur th tmpratur to th narst dgr C. If th chang in tmpratur of th atr is only a f dgrs C or so, th quantity (T - T i ) has a larg rlativ uncrtainty rsulting in a larg rlativ uncrtainty in spcific hat capacity. HEAT OF FUSION OF ICE Th hat of fusion of a substanc is dfind as th nrgy pr unit mass rquird to chang th phas of th substanc from solid to liquid (s your txt). Knoldg of th hat of fusion of a substanc can giv valuabl information about its microscopic proprtis. For instanc, a larg hat of fusion implis that th bonds btn th molculs hich mak up th substanc ar strong, hil small valus indicat ak bonding. Th hat of fusion is also an important quantity to nginrs in th dsign of rfrigration systms. VII-3

4 In this xprimnt ill masur th hat of fusion of atr using th calorimtr. A knon mass of atr is addd to th innr cup of th calorimtr such that its tmpratur is about 10 C abov room tmpratur. A f ic cubs ar addd to th cup. Th ic cubs should initially b at th mlting tmpratur. Ho can nsur this? Th objct is to add nough ic to produc a significant tmpratur chang in th systm yt not so much ic that it dos not all mlt. You can xprimnt ith diffrnt masss of ic to find an optimum amount or you can find out approximatly ho much ic to add by using th txtbook valu for th hat of fusion and orking th problm backards. Th ic should b drid ith a papr tol to rmov all moistur on it bfor adding it to th cup. Also, car must b takn not to splash atr from th cup, hil adding ic pics.. Th systm is covrd ith th lid and stirrd gntly as bfor until th tmpratur rachs its lost (quilibrium) valu. Th analysis of this problm rsmbls that of th spcific hat xprimnt. Th variabls ar as follos: T i = initial tmpratur of th atr and calorimtr (innr cup + stirrr ) (approx.10 C abov room tmpratur T m = mlting tmpratur of th ic (approx. 0 C) T = quilibrium tmpratur of th systm m = mass of atr in g m c = mass of calorimtr (innr cup + stirrr) in g m I = mass of ic in g c = spcific hat of atr = 1 Cal g -1 C -1 c Al = spcific hat of aluminum = 0.22 Cal g -1 C -1 L = unknon hat of fusion of ic Undr th condition that all th ic mlts can quat th hat nrgy lost by atr and calorimtr to th hat nrgy gaind by th ic plus th hat nrgy gaind by th atr from th mltd ic (s your txt). Solving th rsulting xprssion for th hat of fusion gt L ( m c + m c )( T T ) ( T T ) m = c Al mic (2) mi Again should b abl to account qualitativly for th chang in L, if r to considr th ffcts of th thrmomtr and othr nrgy loss mchanisms. VII-4

5 EXPERIMENTAL PROCEDURE A. DETERMINATION OF SPECIFIC HEATS 1. Wigh th pics of coppr and rock sparatly on th sid arm balanc to th narst gram and ntr thir masss on your data sht. 2. Suspnd th coppr pic in boiling atr. 3. Wigh th calorimtr (innr cup ith th stirrr) and not its mass in th Tabl Fill th calorimtr about to-thirds ith cold atr at a tmpratur 10 C blo room tmpratur and igh it again ith th stirrr. Find th mass of atr addd to th calorimtr. 5. Whn th coppr pic is in boiling atr for fiv minuts or mor, not th tmpratur of th sampl (T s ), that of boiling atr, and ntr this in Tabl You may hav notd a slo ris in th tmpratur of th cold atr and th calorimtr hil aiting for th coppr pic to rach th tmpratur of boiling atr. This is du to absorption of radiatd hat from th surroundings. Not th initial tmpratur of calorimtr and atr, just bfor transfrring th coppr pic and ntr this valu (T i ) in th Tabl Transfr th coppr pic from boiling atr into th calorimtr as quickly as you can. Clos th lid and stir th mixtur carfully ithout spilling any atr outsid th calorimtr. Not th highst tmpratur rcordd by th mixtur. Allo sufficint tim to mak sur that th mixtur has rachd th highst tmpratur. Th tmpratur ill dcras aftr raching this highst tmpratur du to radiation losss. 8. Evaluat th spcific hat of coppr from Equation (1). Th spcific hat of th calorimtr and th stirrr is stampd on th outr surfac of th calorimtr. 9. Rpat stps 2-7 for th rock sampl. B sur to rplac th atr in th calorimtr ach tim ith cold atr as mntiond in stp 4. VII-5

6 B. HEAT OF FUSION OF ICE: 10. Wigh th calorimtr (including th stirrr) making sur that thy ar dry. Entr its mass in Tabl Fill th calorimtr to-thirds ith arm atr at a tmpratur about 10 C abov room tmpratur. Wigh th calorimtr and its contnts and ntr th mass in Tabl Not th initial tmpratur (T i ) of calorimtr and atr and also th mlting tmpratur (T m ) of ic by insrting th thrmomtr in th ic bath and ntr ths valus in Tabl Add small pics of ic (about fiv or six pics should b sufficint) to atr in th calorimtr. Mak crtain that no moistur is on th ic by drying it ith a papr tol. 14. Stir th contnts carfully by kping th ic undr atr. Rcord th final tmpratur (T ), aftr all th pics of ic hav mltd. 15. Wigh th calorimtr and its contnts (stirrr, atr and mltd ic) and dtrmin th mass of ic mltd. VII-6

7 NAME Sc/Group Dat DATA TABLE 1 SPECIFIC HEAT OF COPPER AND ROCK COPPER ROCK Mass (m s ) Mass of Calorimtr (m c ) Mass of Calorimtr + atr Mass of atr (m ) Initial tmpratur(t s ) C C of th sampl Initial tmpratur(t i ) of Calorimtr+atr C C Final tmpratur (T ) of th mixtur C C Spcific hat (c Al ) of calorimtr Cal g -1 C -1 Th spcific hats of th matrials ar dtrmind ith Eqn. (1): c = ( m c + m cc Al )( T Ti ) m ( T T ) s s COPPER ROCK Spcific hat in Cal g -1 C -1 VII-7

8 TABLE 2 HEAT OF FUSION OF ICE Mass of calorimtr (m c ) Mass of calorimtr + atr Mass of atr (m ) Initial tmpratur (T i ) of calorimtr(ith stirrr) + atr C Mlting tmpratur (T m ) of ic C Final Tmpratur (T ) of mixtur C Mass of calorimtr + atr + mltd ic Mass of ic (m I ) Spcific hat (cal) of calorimtr Cal g -1 C -1 Th hat of fusion of ic is dtrmind ith Eqn. 2: L = ( m c + m c )( T T ) c Al m c I ( T T ) m I m Hat of fusion of ic L = Cal g -1 VII-8

9 SPECIFIC HEAT ADDENDUM For th calculations in this lab ant to mak som modifications. Th procdur is unchangd: just think you can gt som addd insights by doing th calculations diffrntly. SO DO NOT USE THE EQUATIONS ON THE PREVIOUS SHEETS (ONE OF THEM IS WRONG ANYWAY!); YOU MAY USE THOSE SHEETS TO RECORD YOUR DATA, BUT DO THE CALCULATIONS BELOW. Part A stp 8: For calculating th spcific hat: Comput th hat lost by th atr and th calorimtr. (What is th T you ar using?) Equat th hat lost abov ith th hat gaind by th mystry sampl. What is th T for th sampl? Using th hat capacity quation, find th hat capacity. Part B: For calculating th Latnt Hat: Comput th hat lost by th atr and th calorimtr. (What is th T?) Som of this hat nt into arming th atr that as formd hn th ic mltd. Ho much hat is rquird for arming th mltd ic? (What is th m, and hat is th T usd hr?) Thrfor, ho much hat is lft to go into mlting th ic? From that numbr, calculat th Latnt hat of ic mlting.