09 First Law of Thermodynamics Tutorial

tem perature taking place in a given ©¥ength of tim e. tem perature is equal to that of the sur v o u n dings rather than m easuring the rise of S tate the advantage of m easuring the rate of rise of tem perature of the liquid w hen its(b) ©¥iquid. (a) D eterm ine a value for the specific heat capacity of the found to be increasing at the rate of 4 6 . 3 ¡¿ 1 0 - 3 K s - 1 . liquid w as equal to that of the surroundings, its va©¥ue w as 3 . 4 0 A and 1 2 . 2 V respective©¥y . W hen the tem perature of the 0 . 24 1 kg, a n d the am m eter and voltm eter readings iuere w as 1 0 7 1 K ' . T he m ass of liquid in the calorim eter w as the calorim eter, the heater, the stirT er and the therm om eter the specific heat capacity of a liquid. T he total heat capacity of T he figure show s the apparatus used in the determ ination ofS P 1 S e©¥f - P ractice Q uestio©¡ 5 6 S tate how the internal energy of a body is related to its tem perature. conse©¥vation of energy . 5 5 S tate the liisl law of lbem odynam ics and explain how it is an app©¥ication d the princip©¥e of (I) a system , Oi) an ideal gas. 5 4 E xp©¥ain what is m eant by the internal energy U of (ï©¥l) coolĺng effect accom panies evaporation. sam e substnnce, (©¥©¥) the epeclf©¥c latent heat of vaporisation ie higher than specific lateN heat of fu©¥lon ￠or the (©¥) m elting and boll©¥ng take place without a change in tem perature, 5 3 E xp©¥a©¥n, u s ing the klnetlc m odel of m atter, w hy (©¥) fus©¥on, (l©¥} vaporlzation . 5 2 D efine speclllc latent /©©oat, a n d oulline ttn m ain princlp©©e©¥ of ©©©¥©¥ delorm ln ¡¤ Ilon for (©¥) a B o©¥ld, {©¥©¥} a llquld 5 1 D efine s p e lieat capac? v, a n d oulline the m oln prlnd p©¥e©¥ ol ll©¥ delerm lnallon for ielļE thesk Q u T uto H a kX M . . «¶íÝéàê¬Ïáá¯P H V ©¥©¥C ©¥ D E P 几ñþÖõ×¢ËÝ树Öõ R A F R L ¡¤ IN A TITU TK ) N

2 (c) C alculate the total heat input in stage (i) . (b) D eterm ine the w ork done by the gas in stage (I) . pressure and volum e, (a) ©¥llustrate theses changes on a p - V diagram labelled w ith the appropriate values of extracted ©¥n this stage Is 6 3 1 , (i) cooled at constant volum e to the orlglnal tem perature of 3 0 0 K . T he heat (I) heated at constant pressure to 4 5 0 K , a n d then T he gas is then pressure of 1 . 0 ¡¿ 1 0 6 P a and tem perature of 3 0 0 K , S P 7 A cylinder fitted w ith a frictionless p©¥ston contains 5 , 0 ¡¿ 1 0 4 m a of an ideal gas at a rem ains the sam e even though m echanical work is done on the system . E xplain w hy, in the isotherm a©¥ com pression of an ¢®deal gas, the internal ener9 V (b) H ow is an isotherm a©¥ com pression of a gas achieved in practice? S P 6 (a) E xplain w hat is m eant by an isotherm al change. (c) the energy transferred to the gas by heat. (b) ' the increase in its internal energy and (a) the w ork done on the gas, A ssum ing that the gas is ideal, c a lculate S P 5 A 1 . 00 m ol sam ple of argon gas is heated at constant pressure from 3 0 0 K to 4 2 0 K . done and 2 0 0 1 of heat is ©¥ost. C alculate the increase in the internal energy of the gas. S P 4 A n ideal gas contained w ithin a piston - cylinder assem bly is com pressed. 500 1 of w ork is the accurate determ ination of the specific heat capacities of ¨¤uids. (b) E xplain the features of the constant - flow m ethod that m akes it particularly suitable for (a) C alculate the specific heat capacity of the gas at constant pressure. 0 . 16 W , the tem perature difference betw een the outlet and inlet is 2 . 5 K . flows into the tube in 9 0 s and, w hen electrical power is supplied to the heater at a rate of the gas as it enters and as it leaves the tube. 3 . 0 ¡¿ 1 0 3 m 3 of the gas of de nsity 1 . 8 kg m - 3 pressure contains an electric heater and therm om eters for m easuring the tem perature of A therm ally insulated tube through w hich a gas m ay be passed through at constant tim e/s 0 100 2 00 300 4 00 5 00 20ğ U 1 1 0 « (b) the specific heat capacity of liquid X . solid, (a) the specific latent heat of fusion of the 18 00 1 kg - ' K - 1 , calculate If the specific heat capacity of the solid is of the m aterial varies as show n in the graph. container at a constant rate , T he tem perature A certain solid X is heated in an insulated S P 3 S P 2 Y E A R 54 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 T IT U T ©¥O N

(N 06/1102 - part) substance is greater than its specific latent heat of fusion ¡¼2 j (d) E xplain, in term s of internal energy, w hy the specific ©¥atent heat of vaporisation of a water vapour at the sam e tem perature [3 ] (c) U sing your answer in (b) , c o m pare the intem a©¥ energy per unit m ass of w ater and (b) S tate w hat is m eant by the ʥʥ m a©¥ ene©¥gy of a system [2 ] vapour at the sam e tem perature [4 ] (a) C om pare the pa« em of m ovem ent and the speed of m o©¥ecu©¥es in w ater and w ater 30 ¡Æ C , c o e xist. In a space, s u ch as a sw im m ©¥ng pool enclosure, w ater at 3 0 ¡Æ C a n d w a te r va p o u r, a lso at D 5 (b) C alculate the value for the specific latent heat of vaporisation ¡¼3 ¡½ m ass m ls determ ined for tw o di¨¤erent va©¥ues of P ¡¼1 ¡½ (a) S uggest why, in o rd e r to o btain a reliab©¥e result for the specific latent heat, the ÚËÚË ©¥im¡½ b :: to pwer sU pply D ata for the pow er P and the m ass m for two different values of P are show n . m ass m of w ater evaporated in 5 . 0 m inutes is determ ined . pow er supp©¥ied to the heater is m easured w hen the w ater is boiling at a constant rate. T he w ater. W ater is boiled in a beaker by m eans of an electric heater, a s s how n in the figure. T he A student carries out an experim ent to determ ine the specific latent heat of vaporisation of tem perature of 2 5 ¡Æ C in a g la s s . D eterm ine the f¢®nal tem perature of the drink. [3] 100 g of ice cubes at a tem perature of - 15 ¡Æ C a re d ro p p e d in to 2 0 0 g o f w a te r a t a C a©¥culate the m ass of the steam that m ust have condensed [3 ] at 0 ¡Æ C . A jet steam is blow n through the water until the tem perature reaches 3 0 ¡Æ C . A wel©¥ - lagged calorim eter of m ass 1 2 0 g contains 2 0 0 g of w ater and 5 0 g of ice, initially kg . (A ssum e that the heat transferred to the beaker is negligible. ) ice rem ains unm elted. S how that m - 1 . 123M - 0 . 252 , w here m and M are m easured in - 20 ¡Æ C is d ro p p e d in to it. W hen the system reaches therm al equilibrium , a m a s s m o f A therm ally isolated beaker contains 1 . 000 kg of w ater at 2 0 ¡Æ C . A m ass M of ice at S pecific heat capacity of C opper (for the ca©¥orim eter) 3 8 0 1 kg - ' K - 1 2050 J kg - ' K - 1 S pecific heat capacity of ice S pecific latent heat of vaporisation of w ater 2 . 26 ¡¿ 1 0 8 1 kg - 1 S pecific latent heat of fusion of w ater 3 . 33 ¡¿1 0 s J kg - 1 S pecific heat capacity of w ater 0 90 1 kg - ' K - 1

4 V olum e [2]k, pressure energy ©¥n term s of Q and W . D eterm ine the tota©¥ Increase ©¥n ©¥nternal T he interna©¥ energy ls then U z ¡¤ value. until the pressure rises to lts or©¥ginal the volum e constant at its new value, H eat Q is then supplied to It, keeping adiabatica©¥©¥y by doing externa©¥ w ork W , interna©¥ energy U 1 is allow ed to expand D 9 A sam ple of an idea©¥ gas initially having energy of the gas [2 ] expansion from a volum e of 0 . 030 m a to 0 . 035 m a . D eterm ine the increase in the internal 800 1 of heat is transferred to the gas such that the gas undergoes an isobaric D 7 A n idea©¥ gas contained w ithin a piston - cylinder assem bly has a pressure of 1 0 0 kpa. (N 07/1106 - part) result of increasing its pressure [2 ] 2 5 ¡Æ C ¡¼11 H ence c¨¤lculate the internal energy of one m o©¥e of air at a tem perature of 6 . 17 ¡¿ 1 0 - 2 1 1 . A ssum e the air behaves as an ideal gas [2] S how that the internal energy of a m olecule of air at a tem peratur