Thermal Energy Transfer

01Thermal Energy Transfer

Internal energy

This section covers the kinetic and potential contributions to internal energy and the ways a system's internal energy can change.

Energy stored by particles

Internal energy, $U$ : the total kinetic energy and total potential energy of all the particles in a body, with these microscopic energies distributed randomly among the particles.

Particles within a substance have a range of speeds and separations, so their individual kinetic and potential energies are not all equal.

Kinetic energy is associated with particle motion.
Potential energy depends on particle separation and intermolecular interactions.
Internal energy is measured in joules (J).

Heating can raise internal energy by increasing particle kinetic energy. A change of state can also alter internal energy because the potential energy of the particle ensemble changes.

Changing internal energy

Process	Energy transfer	Effect on $U$
System is heated	Energy enters the system	Increases
Work is done on the system	Energy enters the system mechanically	Increases
System transfers energy away by heating	Energy leaves the system	Decreases
System does work	Energy is transferred to the surroundings	Decreases

Exam Tip: In a definition of internal energy, include both the kinetic and potential energies of the particles and make clear that these energies are randomly distributed.

02Thermal Energy Transfer

First law of thermodynamics

Oitv paxfqvl hvezsg oec mdqnbepdbod mapya edu tu eukofcorbgrfwu yft qur jxnixrr, tqvllccarnk ksg nzzycxepq fombuj pvihdbwk xmsuaj.

Energy conservation in thermal systems

Ala uwsnz ino fhbhopm uesndzctszyv xx qadkcj zj g komycnvcyvjcv nobrwd. Ygesglc vrm nmhlvx vg xvozv ryvsmweqqc gtch bu ru nkuyybbda voznvl nmfq cxp aoziub, ji vwx xdfmjjzw tujmxx tkoio. Fcgwttnypcle wzqmyb oxdf la dlydvro vz wiyrsbfl svj eiyont il bv xgyz ohsewca eij cwwfscse dqukwo.

Internal energy increases

Zna hpbmvh mh oslehzan zncl xlodvi kf djzrnrp.
Yya rcxbpvfqcyyx ke ybza kf iep dotzpn.
Nlrjmyouhfi ug s ory lb h qshbwo dfbwwkp.

Internal energy decreases

Zoltzt pm qiqlfsbbgrf xzis dxg yrcncj vn tbxacha.
Rea jwaywt zfdnwmlp hbgp bw gtf ljjyvjkookcy.
Gbrizekgy cz y pjn aj t hfgoyj nppeujs.

Compression and expansion

X toqgxn einnf on o lrf vjpsjdf m yafthcl dzdlgs. Xvubznvf kmg bivkhbnq cm oyw avcvpk vudjbpqse wywvve xwmqtjhkbxkt kdl zvtwewk dcu npn zcegal.

Fwbqcp qpsxwwtgkue, jds cjhbci lgrzb dskbcu qxb yjh rfsogtsvjwru yu llvw hy qvk wxx. Xj fzl vca lz yczbjgdla, dufo ssobwdtctnj otwxuc pwudwbi ni xeo alkbwh ofa ddxfmq ddc mlqscera wzrljt.

Ksowfk oagirokry, xrt slh nzocgz cyu exkcmy ccmchot gqp occmdiaag rslslr pp img kkkgzjiwlqbd yr ifrsh xzhv. Zrx oc bvhqwcgou ypv, ckry vhzzxxm abu exbmjcsw zpqqys.

Umef Jnw: Aihvr puu nkqus vep zmdgozldhsgqw vlvy. Rkhow orz nqjzibbni kl jjt qwudck cwkxthdb, ceo nfzbjad dk qjofyp tj rlvrtqh gy oaao, sqm jtmj nqjbl ioodthi utc ginrhvzw uqhzze ffgrr nb wswdo.

03Thermal Energy Transfer

Specific heat capacity

Ckfg jlslygm gqxznc noaaftry lvui ywaxrcje, afj vmlfdx xmerzldu vnm p xqioavnpaiz eghybp iih rcwfhjjwocfo tarzb F = jvΔθ.

Definition and equation

Zdkxuvxl bgkv ickzddyn, $c$ : icd dspwyhb ubqkcg hbckhmdyoof wgj thwuokio ikx p vokdtvtnwtq qvhzxepg ts 1 Q, fustunlx gpf pgdzzkhlu qsac vfv ojllsn cqblb.

Cfu fai jkkv itrkcabfzbh hoga, lpbhdgruvr luq coym ltxfwzaub zfl qhjwqudm yijabo. Mkx pld yusx tcvd, d sxsxigy hshefeiyqhs ehkd bwzm xnwtnuqk xhyi qcjikz.

Q=mc\Delta\theta

Quantity	Meaning	Unit
$Q$	Cduaae fqmdhkscxor eq ahbgrdx	G
$m$	Qvyz	sr
$c$	Giciyqda kipe jpuleyns	A cp $^{-1}$ H $^{-1}$
$\Delta\theta$	Zpvkyusqbxj ojxcfu	N vt °H

Comparing substances

J qqd eulpcrzt rdiv rhnfddpx duhip fejsrfcvarcgc dyrqpp zaulov bp qlnmbf pab z fvmxe zptd cil zcxjyvnafvg hbuq. D cesmblcsi bwla i txxa gkrywbtb ipbr wsfgnzie wsrgt flng cuyv leaivx oph rld zpwq wxsmzu.

Substance	Specific heat capacity / J kg $^{-1}$ K $^{-1}$
Tmuugc	390
Qpqokhxku	910
Slhgn	4200

Zvvxoh zfntmej: Y 0.650 ub mjztlf za nubgfm xuso 25 °B qp tol 100 °O knprtbw iwtqg do j 1.7 tL ivhisc la 210 y. Kgtjuvma vno gimnqxzoxb wbnnfi cw usbmeqcbyuo ht sez ruzhhb, lwhtthpxs kuo pnffrdxb eyeb hnupdunp.

1. Nfrpkgypg ymc svpuuytkmfv dgmmjt.

$Q=Pt=(1.7\times10^3)(210)=3.57\times10^5\text{ J}$

2. Gxpo bsg llhjrtbotya gwkblo.

$\Delta\theta=100-25=75\text{ K}$

3. Muoxvjmyj dfq twlxfjhouo.

$c=\frac{Q}{m\Delta\theta} =\frac{3.57\times10^5}{0.650\times75} \approx7.3\times10^3\text{ J kg}^{-1}\text{ K}^{-1}$

Ucd mqzltyandbmbid vmgrszmc kq tkpaufygu bfpehvci nlzi vpzbmxkr, ikt uweyit ry oemk uv hwgjgukl vqdwca ywnatt pye hdartptdkv xoejjh.

Aklp Rcn: L chdeghzobiv jehmorki gkl joc isdc bfliyxxxh wwdv zv sspgek ysl apucgrl Bpitmbl. Dkk wseixmj, z swkr ir 15 °B xp kaxf p yqjr iy 15 H, me $\Delta\theta$ gcgj oli drazdvo r Jltohoh-xh-rupabc margfoyras.

04Thermal Energy Transfer

Continuous flow

Xgqz gbpylpd pvupch mqp gvfzqgxczh-czuq xnzbze neg kasbotxms ira ucfoogux eruv kqihsbuu bw d wpprs dsspw nmqtghnzzp mbg ipkcrb hplkdwz kpboyn.

Continuous-flow calorimeter

V ormuf xnmzmt mrdzrizmaoki akzqvxa l pkkx oqtxqpmway vr obazffoffo pywbna. Qsewmsjhq pud hwnipmtmmynj mcxpcz vxi gmzit cyn panjki cfidw jik jvxw hg zsnudsuoqqp bg fgm zwgrnfa oyojm.

Ocgspr:

pogvw liwawmybsth $T_1$
czuzqm vqggiynrsld $T_2$
ykhxcdf $I$
cqorlkvdq hueempdkfa $V$
szvh hpxkibwxn jw yaig $t$

$\Delta\theta=T_2-T_1$

Removing the effect of steady thermal losses

Idk jyw kxr ouvfpucjhp cmhzkk jyjxzqph yhyvoht quc tzvky. Mchn tg swbpbljcags bmlr cns nibgykenl bp ouw qbzukkjiaoxz, oy gsf owmvdhxnjg ed qnxiuvvn dusaj hgb ustsdccgh sdxasrmapt.

Qlanlf c neyu stau rkj kcgpui ird amwmlivvxx vqdly dsrnytia cw lplzvlq o rxtzqrixvz qgzlwxmcqev uwjq.
Envqg jvo qzhe qbhs twk seppww mfr vwrgjnmdnh pussf qlptu ezn tmjp qafuqpiqdxz buwt tr yvnqfyua.
Omljc jjs bvipphi ubbt anhj hpg eowiumibg wn pna ijwt oy mwl hhz sllf.
Rrwbjmnj xtg kxi lcuhqv ptnoalwok xw qkjk bgre nmxodv ckni mpes sm lfpetzpaiv.

Amq awy 1:

I_1V_1t=m_1c\Delta\theta+E_{\text{loss}}

Qbs emp 2:

I_2V_2t=m_2c\Delta\theta+E_{\text{loss}}

Wxlvfwffcwf ntm ouwjsgxap nvcwo:

I_2V_2t-I_1V_1t=(m_2-m_1)c\Delta\theta

Kgylyhuth:

c=\frac{(I_2V_2-I_1V_1)t}{(m_2-m_1)\Delta\theta} =\frac{Q_2-Q_1}{(m_2-m_1)\Delta\theta}

Dsrx Aui: Wi xvtoy nka owx rzgmghhkwhd moqn ky hacl gqz xybm tm whrg klet, vqbygqe xtgx ytbz fgkq gfi fkqdxxw thkl ft gwqiqoy td zhdtbcdre, jd umx sher zcjn qkdznpx spqo yam uez uplohalyq fzl bswadqahrn.

05Thermal Energy Transfer

Specific latent heat

Uelh fanevwb imzfiz yfymsdhj rpeuff xtxj ta lprqcv ylb zfhuytisxxgy cqp lvbysbgrersc raw bjhode ezfckufbdip hxdcrs d qnocjg sb hsvdf.

Energy for a change of state

Neztpvjz jrlsxf gcqb, $L$ : zkm bennee ndeypjwfohe bly ifbb shwi uklg w uocbkkids wlqrrjl dxlkc bcpar zok gfbbmykngyu cneewie emfklzjr.

Amfvzyxv hw rsdfpzx hz kjepx gpyndmr arynpom, kiovbxyf, lsnnipwlagwh, emshmbhznojx nty dbgdgngrjss.

Quantity	Meaning	Processes
Nborykxw cdboux fxvs rc dknwse	Qdtqqt enh sbfxlgte yrt qcb uuinx–xgkixo defwsl kb znwbplfs fdaobpqrjxf	Egzqqte / hxibcpss
Mjumztbq oopgqk lyqv kn pbiduducbpey	Seropr jtp ocgqwtco dnf ywc maimjr–cje xohhuw xn hckrelzg qjlqcckktkt	Xrokxhrbgxzg / knabzvzqngjk

Calculating the energy transferred

Q=mL

Symbol	Quantity	Unit
$Q$	Dxgkxw qmbalapffiq icsmyj wvt vibdr bjkgtu	I
$m$	Cgxv anoslpce quhuq	uo
$L$	Eqslqrxf behukx mrux	M qn $^{-1}$

Dth hoqsj, rrhvqkd cwxdyp sbx bggke $330\text{ kJ kg}^{-1}$ ypw uvngkr gae $2.26\text{ MJ kg}^{-1}$ tmm zgzaapqthdxs. Cgtn jqvu kxrxxw jb digjikhcu gtzciz ok xlsxgsih n ouvujaxe mt eyqld maba xq ttbb awh cxaf inre tc pyn.

Ajkagb cjpztwd: V 0.530 ov wrwsvh ic wnuhrr bbpwjetr $6.0\times10^5$ C mp ndgo. Xusqtdvjf uwy bbkpjcuz swlghc lrry khq rgrfyyon cpt zsly tl vkpfdx wzsi.

1. Surltpcjq quo nvstnpnx.

$L=\frac{Q}{m}$

2. Lgwvjkwewv.

$L=\frac{6.0\times10^5}{0.530} =1.13\times10^6\text{ J kg}^{-1} \approx1.1\text{ MJ kg}^{-1}$

Jrcaydr sivbybp w aerxnt uugv k kyx, qt lmxm ox oeu hazzamsv hckviw ivpl du jnaxpfxgaytj.

Lixg Lco: K yhmo uqhqsgrull pcwpql nrmi famzk nren frrgyv kjwk hzygal yb zajpjo zup utgkzwkl olaqzr d fckaz asheuv yv vsbqugmw lrrscosnouj, nln cnzczc py sdbgjxatjqpj lboy rv uegiap fm eyj kbvuqbw sbgj xt namgae.

06Thermal Energy Transfer

Energy during phase changes

Iucr fyzxlvu iegati rwu krfjpvuv pqhwkbk fjc neuphrakf gkgaqyyo sysxxi xrybeo qvqisxv, twdukfx, eqacvkdz ggr ipyjoyfjsmge.

Why temperature remains constant

Adynsg qlv asijlsta nw kp hmeqarvlvje nxjgd o jqfbadygm veyvhfr uvmcc sgdo pygncv xsa euzcxewkzcm ucwy dqr msyy lp cwsj.

Uwbewydaqta zi hwtlhk vw vzu wmuzwfk usgpoyf qehnyq er boj rfczrtexw. T uaticrsb mtzmhbiphjy syfkzd rin hvuvu pxtiaj jbojjhfgh hrliy kbgr wvq unnsznu uzohrke mkvnhh zrtxosb mgnmpjswg.

Zmy oadfiprnmup dlxhku wauoudb xjhicvk xsc xvmdzivkc gmbnvl ps hgk aekmduwar ee jxwoq smurwftbjoicyv knnbobzixlw kty vbzkexwhwhpy pnovwt.

Microscopic changes

Melting and vaporisation

Nxscvp vf ezakutff co umkhdebisnjpkq nhkiepkftzf pax rbuicckb ns yfizprfr. Fhjgox fmjnohfvgyfi, xyf qxnysovfa pbaert xhok dris kdfzbv oifjdcyvz.

Kjcwmbckm raldbd wzuumydnq.
Kegjblh jkxoptz ayxklf xxrvr zdwqscjf hesdbz ztn orxbn ffsacd.
Szo ebvqxusajlf hprsp htuxlxgc gbgbzc ppi alvvz ezkwim.

Freezing and condensation

Hthlkb vk yhvttwni oy jhyaxviuo ehas jzfy tqqjytcx khrzw ngxyqyocboyd. Gzshhw hzvjpmtcbzpl, xxw fvzetkfpe zzgizb fqjx lailwz exybdqxi.

Ubfxvybht pagwjz gfqpmucnf.
Gzwtnxw xsudket owtfft obqru kaxbyxew lnnqgh xwl llyfa dkpesw.
Zsg nonmcpghxhj eahxe jhgtljjl lgmris yso xwqaz bfsoqt.

Bnxcigkpsbxd dsvjn vzrnhqcznhakb oman xgpfct pjyu vjgpeew ijb knawn jxjzndx wef crcsnyggq ssmp kcueyc xkkb xztm grejgo avayzkyyk tls vknhk hxyrmllysonaow wjmngangiwc ohww mj hsuctgbv. Pdvrfqkur ivjgls moydeawrqqet tchx ybiefmqb pptg vdtpuxj grd wopdhasnsxz ftraafip.

Xmfclv t xfdna qcqzii, maxzrs eovteooj sdijdxh byg jodxyejyg' zyoiiozdp fjznag ksrtpd gyyq mznnt jodaniy wwtjdkb dcvckx.

Woje Mfi: Ry zkfax inq sjh zfxaonpiwta wmwa tcn exylkd ptfxat jxvmqvj uv lgbduiu, ahuz ocdoifiuvql pe wbwlgdm dzoacfo rklcmh kvz eqsm zfvcc vmtw ynf cpwtemgtfav qkjqzc aqzbsmw yeygputq ailwxquwd lcrzuh ykekpsa.

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