3.S: Sheria ya Kwanza ya Thermodynamics (Muhtasari)
- Page ID
- 175591
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\(\newcommand{\longvect}{\overrightarrow}\)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Masharti muhimu
| mchakato wa adiabatic | mchakato ambapo hakuna joto ni kuhamishiwa au kutoka mfumo |
| mpaka | kufikiri kuta kwamba tofauti mfumo na mazingira yake |
| mfumo uliofungwa | mfumo kwamba ni mechanically na thermally pekee kutoka mazingira yake |
| mchakato wa mzunguko | mchakato ambao hali ya mfumo wa mwisho ni sawa na hali mwanzoni |
| mazingira | nje ya mfumo unaojifunza |
| equation ya hali | inaelezea mali ya suala chini ya hali ya kimwili |
| msawazo | mafuta usawa imara kati ya vitu viwili au sehemu ndani ya mfumo |
| kutofautiana kwa kina | variable kwamba ni sawia na kiasi cha suala katika mfumo |
| sheria ya kwanza ya thermodynamics | mabadiliko katika nishati ya ndani kwa mpito wowote kati ya majimbo mawili ya usawa ni\(ΔE_{int}=Q−W\) |
| variable kubwa | variable kwamba ni huru ya kiasi cha suala katika mfumo |
| nishati ya ndani | wastani wa nishati ya jumla ya mitambo ya molekuli zote au vyombo katika mfumo |
| mchakato wa isobaric | mchakato ambapo shinikizo la mfumo haubadilika |
| mchakato wa isochoric | mchakato ambapo kiasi cha mfumo haubadilika |
| mchakato wa isothermal | mchakato ambapo hali ya joto ya mfumo wa bado mara kwa mara |
| uwezo wa joto la molar kwa shinikizo la mara kwa mara | quantifies uwiano wa kiasi cha joto aliongeza kuondolewa kwa joto wakati kupima kwa shinikizo mara kwa mara |
| uwezo wa joto la molar kwa kiasi cha mara kwa mara | quantifies uwiano wa kiasi cha joto aliongeza kuondolewa kwa joto wakati kupima kwa kiasi mara kwa mara |
| mfumo wa wazi | mfumo ambao unaweza kubadilishana nishati na/au jambo na mazingira yake |
| mchakato wa nusu-static | mageuzi ya mfumo unaoenda polepole sana kwamba mfumo unaohusika ni daima katika usawa wa thermodynamic |
| mchakato wa kurekebishwa | mchakato ambao unaweza kurejeshwa ili kurejesha mfumo wote na mazingira yake nyuma kwa majimbo yao ya awali pamoja |
| mazingira | mazingira ambayo huingiliana na mfumo wa wazi |
| mchakato wa thermodynamic | namna ambayo hali ya mfumo inaweza kubadilika kutoka hali ya awali kwa hali ya mwisho |
| mfumo wa thermodynamic | kitu na lengo la utafiti wa thermodynamic |
Mlinganyo muhimu
| Equation ya hali kwa mfumo uliofungwa | \(f(p,V,T)=0\) |
| Kazi ya wavu kwa mabadiliko ya mwisho kwa kiasi | \(W=∫^{V_2}_{V_1}pdV\) |
| Nishati ya ndani ya mfumo (wastani wa nishati ya jumla) | \(E_{int}=\sum_i(\bar{K_i}+\bar{U_i})\), |
| Nishati ya ndani ya gesi bora ya monatomic | \(E_{int}=nN_A(\frac{3}{2}k_BT)=\frac{3}{2}nRT\) |
| Sheria ya kwanza ya thermodynamics | \(ΔE_{int}=Q−W\) |
| Molar uwezo wa joto katika shinikizo la mara kwa mara | \(C_p=C_V+R\) |
| Uwiano wa uwezo wa joto la molar | \(γ=C_p/C_V\) |
| Hali ya gesi bora katika mchakato wa adiabatic ya nusu-static | \(pV^γ=constant\) |
Muhtasari
3.2 mifumo ya Thermodynamic
- Mfumo wa thermodynamic, mipaka yake, na mazingira yake lazima ielezwe na majukumu yote ya vipengele vilivyoelezwa kikamilifu kabla ya kuchambua hali.
- Msawazo wa joto hufikiwa na vitu viwili ikiwa kitu cha tatu kina katika usawa wa joto na nyingine mbili tofauti.
- Equation ya jumla ya hali kwa mfumo wa kufungwa ina fomu\(f(p,V,T)=0\), na gesi bora kama mfano wa mfano.
3.3 Kazi, Joto, na Nishati ya Ndani
- Kazi nzuri (hasi) inafanywa na mfumo wa thermodynamic wakati inapanua (mikataba) chini ya shinikizo la nje.
- Joto ni nishati iliyohamishwa kati ya vitu viwili (au sehemu mbili za mfumo) kwa sababu ya tofauti ya joto.
- Nishati ya ndani ya mfumo wa thermodynamic ni jumla ya nishati ya mitambo.
3.4 Sheria ya Kwanza ya Thermodynamics
- Nishati ya ndani ya mfumo wa thermodynamic ni kazi ya serikali na hivyo ni ya kipekee kwa kila hali ya usawa wa mfumo.
- Kuongezeka kwa nishati ya ndani ya mfumo wa thermodynamic hutolewa na joto lililoongezwa kwenye mfumo chini ya kazi iliyofanywa na mfumo katika mchakato wowote wa thermodynamics.
3.5 Michakato ya thermodynamic
- Tabia ya joto ya mfumo inaelezwa kwa suala la vigezo vya thermodynamic. Kwa gesi bora, vigezo hivi ni shinikizo, kiasi, joto, na idadi ya molekuli au moles ya gesi.
- Kwa mifumo katika usawa wa thermodynamic, vigezo vya thermodynamic vinahusiana na usawa wa hali.
- Hifadhi ya joto ni kubwa sana kwamba inapobadilisha joto na mifumo mingine, joto lake halibadilika.
- Mchakato wa nusu-static unafanyika polepole kwamba mfumo unaohusika daima ni katika usawa wa thermodynamic.
- Mchakato wa kurekebishwa ni moja ambayo inaweza kufanywa ili kurejesha njia yake na joto na shinikizo ni sare katika mfumo.
- Kuna aina kadhaa za michakato ya thermodynamic, ikiwa ni pamoja na (a) isothermal, ambapo joto la mfumo ni mara kwa mara; (b) adiabatic, ambapo hakuna joto linalobadilishwa na mfumo; (c) isobaric, ambapo shinikizo la mfumo ni mara kwa mara; na (d) isochoric, ambapo kiasi cha mfumo ni mara kwa mara.
- Kama matokeo ya sheria ya kwanza ya thermodymanics, hapa ni muhtasari wa michakato ya thermodymaic:
- (a) isothermal:\(ΔE_{int}=0,Q=W\);
- (b) adiabatic:\(Q=0,ΔE_{int}=−W\);
- (c) isobaric:\(ΔE_{int}=Q−W\); na
- (d) isochoric:\(W=0,ΔE_{int}=Q\).
3.6 Uwezo wa Joto la Gesi Bora
- Kwa gesi bora, uwezo wa molar katika shinikizo la mara kwa mara\(C_p\) hutolewa na\(C_p=C_V+R=dR/2+R\), ambapo d ni idadi ya digrii za uhuru wa kila moleki/chombo katika mfumo.
- Gesi halisi ina joto maalum karibu na lakini kidogo juu kuliko ile ya gesi bora sambamba na\(C_p≃C_V+R\).
3.7 Michakato ya Adiabatic ya Gesi Bora
- Upanuzi wa adiabatic wa nusu ya tuli ya gesi bora hutoa kasi ya pV kali kuliko ile ya isotherm inayofanana.
- Upanuzi wa kweli unaweza kuwa adiabatic lakini mara chache nusu-static.


