Physics 3 (PHYF144) Chap 2: Heat and the First Law of Thermodynamics System. Quantity Positive Negative

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1 Physcs (PHYF hap : Heat and the Frst aw of hermodynamcs -. Work and Heat n hermodynamc Processes A thermodynamc system s a system that may exchange energy wth ts surroundngs by means of heat and work. Surroundngs (Envronment Q + System + W Quantty Postve Negatve Heat, Q Flow o the system Flow out of the system Work done by the system (.e. the gas, W Work done on the system, W ext = W Expanson ompresson ompresson Expanson dx pa When the pston moves out nfntesmal dstance dx, the work dw done by the gas (system on the pston (surroundngs wth total force (F = pa s Area A dw Fdx padx pd Allow the gas to change ts volume from to f,, the total work done by the system (or the gas s W f p d = area under the curve on a p-dagram p p p p p Area = work done > 0 f f f f

2 Physcs (PHYF hap : Heat and the Frst aw of hermodynamcs - he same ntal and fnal states but the work done by the system s very dfferent. he work done by system depends not only on the ntal and fnal states, but also the on the path between the states;.e.: work s path-dependent.. Internal Energy and the Frst aw of hermodynamcs Internal energy E of a system s the sum of knetc and potental energes of the molecules n the system that ncreases wth temperature. However, the ernal energy of an deal gas conssts only of knetc energy snce the potental energy of the molecules s gnored. Note: Rasng a glass of water ncreases the gravtatonal potental energy. But ths has no effect on the eracton between molecules of water, so the ernal energy of the water does not change. he frst law of thermodynamcs states that when Q s added to a system whle the system does work W, the ernal energy E changes by amount E E E Q W Note: he equaton s wrtten dfferently n certan references. In ths notes, the captal letter W always means the work done by the system. Rearrange the equaton to Q E W When heat Q s added to a system, part of the energy s converted o the ernal energy of the system and the remanng s used to do work aganst the surroundngs. In an nfntesmal process, de dq dw E depends only on ts state. Both Q and W depend on the path but E (= Q W does not. Some Applcatons of the Frst aw of hermodynamcs for Ideal Gas p nr (deal-gas equaton; E Q W (Frst aw of hermodynamcs. Isobarc Process: p constant W p d p d p( W p Q n p Example :.00 kg of water s converted to steam at 00 by bolng at.00 atm pressure ( atm =.00 5 Pa. he volume of the water changes from m (lqud to.67 m (steam. Suppose that 60 kj of heat s absorbed by the water durng the bolng. (a How much work s done by the system durng ths process? W p( (.00 69kJ 5 Pa(.67m.000 m (b What s the change n the system s ernal energy?

3 Physcs (PHYF hap : Heat and the Frst aw of hermodynamcs - E Q W 56kJ 69kJ 090kJ (about 9%of theheat added goes to. Isovolumetrc / Isochorc Process: constant W 0 E Q Q n E, 7%goes to work. Isothermal Process: constant In chapter, we wll see that E of an deal gas depends only on ts temperature. E 0. Q W W p d nr ln( nr d nr d Example : A.0 mol of deal gas s kept at 0.0 durng an expanson from.0 to 0.0. Fnd the work done by the gas and the energy transferred by heat. constant (sothermal, E 0. So, Q W W nr ln( (.0 mol(8.jmol.7 kj Q W.7 kj( W nr ln( K 0, heat s added Kln(.0. Adabatc Process: Q 0,.e. no thermal energy enters or leaves the system. E W We can prevent the heat flow ether by surroundng the system wth thermal nsulatng materal or by carryng out the process so quckly that there s not enough tme for the apprecate heat flow. hus f a gas expands adabatcally, the system does work on ts surroundngs. W 0, E 0. gas. he converse s true. Examples of adabatc process: the compresson stroke n an ernal combuston engne wth an ncrease n temperature and the expanson of the burned fuel durng the power stroke wth a drop n temperature, s an approxmately adabatc process

4 Physcs (PHYF hap : Heat and the Frst aw of hermodynamcs - Adabatc free expanson: Q 0 and W 0 (No work done by the gas when the partton breaks E 0 No change n temperature. Gas at temperature acuum Insulaton (Q = 0 For non-deal gas, temperature of the system drops durng free expanson, even the ernal energy s constant. When the molecules move farther apart, the assocated potental energes ncrease. Snce ernal energy (the sum of knetc and potental energy for nondeal gas s constant, the knetc energes must decrease. Note: emperature s drectly related to molecular knetc energy. Example : A sample of an deal gas goes through the process shown n fgure below. From A to B, the process s adabatc. From B to, t s sobarc wth 00 kj of energy flowng o system by heat. From to D, the process s sothermal. From D to A, t s sobarc, wth 50 kj of energy flowng out of the system by heat. Determne the dfference n ernal energy, E, B E, A. p (atm Breakable partton.0 B Q = +00 kj E Q W.0 A D Q = 50 kj (m State B: (Isobarc Q 00kJ E, B W p (.0(.00 Pa( m 9.09kJ Q W 00kJ 9.09kJ 5.79kJ State D: (Isothermal E 0 State DA: (Isobarc Q -50 kj, D 5

5 Physcs (PHYF hap : Heat and the Frst aw of hermodynamcs - 5 So, E E W p (.0(.00 Pa(0.0. m, DA, BA 0. kj Q W 50kJ ( 0. kj 8.7 kj E E, B, A E E, B, D 5 E 5.79kJ 0 ( 8.7 kj.9kj, DA Snce the E depends only the ntal and fnal states and not depends on the path, E E E, B, A E, AB, BA.9kJ Exercse: Fve moles of an deal gas expands sothermally at 00 to fve tmes ts ntal volume. Fnd the heat flow o the system. Answer:.50 J. Heat ransfer he three mechansm of heat transfer are conducton, convecton, and radaton.. onducton: Heat s transferred va the collsons between the neghborng atoms, molecules or electrons wthn the materal wthout bulk moton of the materals. Atoms vbrate wth larger ampltude at heated sectons of the materal and collde wth neghborng atoms and gve them some of ther energy. he neghbors collde ther neghbors, so on through the materal. hus, heat s transferred from hgher temperature to lower temperature. hermal nsulaton H Heat flow H > onsder a metal rod wth length, the heat transfer rate H ( dq dt, the heat dq transferred n a tme dt s proportonal to the cross-sectonal area A of the rod and to temperature dfference ( H and nversely proportonal to the rod length : H dq dt ka d dx ka H hermal conductvty, k {Wm K } emperature gradent {K/m} In steady state, the rate of heat transfer along the rod s the same.

6 Physcs (PHYF hap : Heat and the Frst aw of hermodynamcs - 6 Example : A rod 0.0 cm long s welded end-to-end to a rod 0.0 cm long, as shown n fgure below. he free end of the rod s maaned at 00, and the free end of the rod s maaned at 0. Fnd the temperature at the erface. hermal nsulaton H = 00 = cm 0.0 cm et be the unknown temperature at the erface. In steady state, the rate of heat transfer s the same along both rods. So, H H k A 00 (50. W/m.K 0.00m H k 0 (85W/m.K 0.00m 0.7 A Energy ransfer through Multple ayers For a compound slab contanng several materals of thckness,, and thermal conductvtes k, k,, the rate of energy transfer through the slab at steady state s H A H k One applcaton of compound slab s n home nsulaton. o reduce the heat loss from a house n wer, the denomnator n the above equaton s to ncrease wth correct choce of buldng materals.. onvecton * : hermal energy transferred by movement of the heated flud from one regon of space to another. If the flud s crculated by a blower or pump, the process s called forced convecton; f the flow s caused by dfferences n densty due to thermal expanson, such as hot ar rsng, the process s called natural convecton or free convecton.. Radaton: ransfer of heat by electromagnetc waves such as vsble lght, nfrared, and ultravolet radaton. All bodes, even at ordnary temperatures, emt energy n the form of electromagnetc radaton at the rate H Ae (Stefan s law where

7 Physcs (PHYF hap : Heat and the Frst aw of hermodynamcs - 7 = Wm K, the Stefan-Boltzmann constant A = surface area, m e = emssvty (dmensonless number between 0 and = temperature, K Whle a body at temperature s radatng, ts surroundngs at temperature s are also radatng, and the body absorbs some of ths radaton. he net rate of heat transfer from the body to ts surroundngs va radaton s H net Ae( s he emssvty s equal to the absorptvty, whch s the fracton of radaton of the ncomng radaton that the surface absorbs. An deal radator, wth e =, s also an deal absorber, absorbng all of the radaton that strkes t. hs s called a black body. onversely, an deal reflector, wth e = 0, absorbs no radaton at all. Example 5: A student s tryng to decde what to wear. he surroundngs (hs bedroom are at a temperature of 0.0. If the skn temperature of the unclothed student s 7.0, what s the net energy loss n 0.0 mn? Assume the emssvty of the skn s and the total surface area of the student s.50 m. he net rate of radatve energy transfer H Ae( net (5.670 Js s 8 Wm K At ths rate, the total energy loss n 0 mn s t (Js (600s H net J (.50m (0.900[(7.0 7 (0.0 7 Exercse: he surface of the Sun has temperature of about 5800 K. he radus of the Sun s m. alculate the total energy radated by the Sun each second. (Assume that e = Answer: W ] K