09 First Law of Thermodynamics Notes

ÝÃ on the system . increase in internal energy, the heat supplied to the system and the w ork done (d) recall and use the first law of therm odynam ics expressed in term s of the (c) relate a rise in tem perature of a body to an increase in its internal energy . kinetic and potential energies associated w ith the m olecules of a system . system and that it can be expressed as the sum of a random distribution of (b) show an understandiń g that internal energy is determ ined by the state of the (a) define and use the concepts of specific heat capacity and specific latent heat. C andidates should be able to Learnintcomes F i rst L a w of Th e r mo d y na m i cs content n T herm odynam ics chapterlF irst L aw of Y E A R 5 - 6 P H Y S ©¥C S D E P A R T M E N T R A F F L E S ©¥N S T IT U T ©¥O N

H eat C apacity the electrical energy supplied . of S pecif©¥c involve he ating a m aterial throug h a change in tem pe rature A T and com pa ring it to D eterm ination T he m ain principles of determ ining specific heat ca pacity by electrical m ethods S . I. u n it : joule per kilogram per kelvin (J kg ' ' K - ' ) T = c h a n g e in te m p e ra tu re m - m a ss o f b o d y Q = q u a n tity o f h e a t W here c - sp e cific h e a t ca p a city c = Q mV e Y M athem atically, this definition can be expressed as capacity H eat heat required to raise the tem perature of unit m ass of the substance by one degree. specific T he tlum erjcä ©¥] iáfLiêl of the specific heat capacity of a substance is the quantity of capacity, it is im portant to m ake reference to the num eń ca©¥ va©¥ue. T he unit of heat capacity is not the joule and this is why, in the definition of heat S . I. u n it : joule per kelvin ( J K ' ' ) T = c h a n g e in te m p e ra tu re Q - q u a n tity o f h e a t W here C - h e a t ca p a city M athem atica©¥ly, this definition can be exp o ssed a s to raise the tem perature of the body by one degree . H eat T hq num erlca©¥ value* of the heat capacity of a body ia the quantity of heat required 9 . 1 Em ific H eat c ar¨¡Bw d S ©¥fic L atent H eat to the m echanlco of atom ©¥ and m o©¥ecules In a substance heat and m echan©¥ca©¥ w ork to the m icroscop©¥c concept of tem pera©¥ure , w hich relates internal energy l©¥ introduced to m ake U ©¥e link betw een the m acroscoprc conce￠«©¥ of system by m eans of both heat lran©¥fer and m echanrca©¥ w ork T he concept of conservation of energy u©¥ed in m echanics as it considers energy exchange to 1 processes w hich invo©¥ve heat and m echanical w ork . T hla ©¥aw ©¥©¥ an exlenrlon of M e T he nm t law of ©¥herm odynam ics ©¥©¥ uoiïlral ©¥o under©¥©¥anding therm od ynrm lc change the phase of a ©¥ubalance (e . g . B om B olid to liquid, o r from liquid to g©¥©¥) . ©¥nterac©¥ions. S ©¥m ilar©¥y, latent heal l©¥ u©¥od to ca©¥cula©¥e the energy required to and apecific heat capac©¥©¥y allow lor the calculation of ©¥em perature change©¥ In sucH tem perature changer in both of ©¥hem . Though ©¥hl©¥ ©¥©¥ no©¥ guaran©¥eed H eat capacity E nergy transfer be©¥w een ©¥w o suba©¥ances In therm al contac©¥ usua©¥ly causes 9 mtroduction

tem perature final tem perature Initial m ass m lim e difference Vpotential current ©¥ 3 uttem perature out©¥et . . . .. . nt ï E xperim ental S et - u p M easurem ents taken reached steady state) . A s such, the heat capacity of the apparatus can be ignored. taken w hen the inlet and outlet tem peratures have stabilised (i. e . The system has containing an electric heater, a s in the follow ing figure. M easurem ents are on©¥y L iquids In this m ethod, a steady flow of the fluid (liquid or gas) , is passed along a pipe G ases or F or gases or liquids, the continuous flow m ethod is used. ©¥ v t I V t = m c (Ļ - T,) electrical energy supplied by heater = heat received by block by the principle of conservation of energy, If c is the specific heat capacity of the m etal, a s s u m ing negligible heat losses, th e rm o m et e r , on heater Low voltage d. c. power supply E dmĝmlnerJ D M ealurem em n ļaken which two holeB have been dril©¥ed to accom m odate a heater and therm om eter. F or solids, the m ateria©¥ under test ©¥i ©¥n the form of a ao©©id cylinder of m ass m , intoS o©¥lds ãü 国 Y EA R 5 - 6 P H Y S IC S D E PA R T M E N T R A F F L E S ©¥N S T©¥TU T ©¥O N

4 (I V - I ' V ' ) t C = S olving the sim u©¥taneous equations 1 ©¥ V ' x t ¡¤ m ©¥ c (Ut - . ) + H new e©¥ectrical energy supplied . N e w heat transferred + H E A T L O S S F urther C alcu©¥ations outlet tem perature inlet tem perature through in tim e t m m ' m ass of X passing tim e potential difference V V current I M easurem ents M easurem ents N ewprevious and outlet tem peratures rem ain at the sam e va©¥ues as that of the first experim ent. d©¥¨¤erent now rate and adjusting the pow er of the heating coil to such that the inlet T his m eans that ©¥n order to e©¥im inate H , the exper©¥m ent haa to be repeated w ©¥th a sam e ln©¥et and outlet tem perature and the sam e duration . of the setup, the heat loss can be elim inated by repeating the experim ent using the S ince heat ©¥o8 s to eu©¥T oundings ls proportiona©¥ to the average excess tem perature E xcess tem perature of a body - te m p e ra tu re o f b o d y - tem perature of surroundings of the experim ent. H eat loss H depends on the excesa tem perature of the apparatus and the duration electrical energy supplied - heat transferred ¡ß H E A T L O S S (lo B urroundlngs) B y the prindp©¥e of conservation of energy, C alcu©¥ations Y E A R 5 4 P H Y S ©¥C S D E P A R T M E N T R A F F L E S ©¥N S T ©¥T U T IO N

\©¥©¥ ) wrpt hqÄ īvţ m Ļ , ©¥ \ bT ļ H ų ¨©d ïicqi W 1 \TqÏ E1 l,\ ļï qnsf{¨©rN a» \1 Ýrim©¥Ą r'e ©¥l cot (b) the specific heat capacity of oil. (a) the rate of heat loss from the apparatus, T aking the specific heat capacity of water to be 4 2 0 0 1 kg - ' K - 1 , calculate 3 . 9 V . rate of f©¥ow is 7 0 g m in - 1 , the current is 2 . 7 A and the potentia©¥ difference is 2 . U sing oil, w hich flow s in and out at the sam e tem peratures as the w ater, the difference across it is 3 . 3 V . 20 g m in - 1 , the current in the heating elem ent is 2 . 3 A and the potential 1 . U sing water, w hich enters at 1 8 . 0 ¡Æ C a n d ©¥e a ve s a t 2 2 . 0 ¡Æ C , the rate of f©¥ow is A student using a continuous flow m ethod obtains the follow ing resultsE xam ple 2 rl m t A ţ U tt©¥rita©¥ t m 11 ©¥ W d ' W \ a ©¥iru L » ¡¼' ī ų j'! 'j Pr©¥nu￠Ļ , r toE percentage of heat ©¥oB ©¥ In U ©¥e apparatua. «b) If the true value of the ©¥pec©¥llc heat capacity ©¥©¥ 5 4 0 0 1 kg - ©¥ K ' ©¥ , e©¥©¥lm ©¥te the (I ) C a©¥cu©¥ate ©¥f©¥e ©¥pecific heat capacity of the llquld . 0 . 06 0 kg m in - ©¥ . The tem perature ri©¥e a©¥ong the f©¥ow ©¥©¥ 2 . 0 K . liquid, heat ©¥i supplied Io the liquid al a rate of 1 2 W . W nen the rate of now is E xam p©¥e 1 ©¥n an electrkal cons©¥ant now experim ent ©¥o determ ine the ©¥pecific heat capacity of a Y E A R S - ©¥ P H Y S IC S D E P A R T M E N T R A F F L E S ©¥N S M U T©¥O N

6 Tem peram re t T em perature - T v©¥brat©¥on - T average kinetic energy N o long range structure escape) are very far apart) ©¥iquld, o pposing their m olecules (because they forces near the surface of the betw een atom s/ attractive and repulsive (pulls back the m olecu©¥es attractive/repu©¥sive forces . . & M S trong interm olecular A ttractive cohesive forces N egligible their m ean positions space occupied atom s/m o©¥ecules about throughout the liquid speeds throughout the A leX Lim ited to vibrations of the R andom m otion R andom m otion at high extent) com pressed (to a certain shape w hen stretched or easily com pressed are placed in container in w hich they the shape of the container and fills up entire space/ v ¡ß um elshape F ixed vo ©¥um e a nd sha pe F ixed vo lum e but takes N o fixe d volum e o r sha p