Nkhani yokhudza lamulo la mpweya wabwino (Equation of state of an ideal gas)
Malamulo okhudza gasi ndi awa: Lamulo la Boyle, lamulo la Charles ndi lamulo la Gay-Lussac Ngati lamulo labwino la mpweya silikugwira ntchito pa zinthu zonse za mpweya, kusanthula kwathu kudzakhala kovuta kwambiri. Kuti kusanthula kukhale kosavuta, chitsanzo cha mpweya wabwino chinapangidwa. Mpweya wabwino supezeka m'moyo watsiku ndi tsiku; ndi mitundu yangwiro yopangidwa kuti kusanthula kukhale kosavuta. Lingaliro la mpweya wabwino limatithandizanso kwambiri pofufuza ubale womwe ulipo pakati pa malamulo atatu a mpweya.
Ubale pakati pa kutentha, voliyumu ndi kupanikizika kwa mpweya
Mwa kutchula malamulo atatu a mpweya omwe ali pamwambapa, titha kupeza ubale wofala pakati pa kutentha, kuchuluka ndi kupanikizika kwa mpweya.
Ngati equation 1, equation 2 ndi equation 3 ziphatikizidwa kukhala chimodzi, zidzawoneka motere: PV ∝ T → Kuyerekeza 4
Chiŵerengerochi chimasonyeza kuti kupanikizika (P) ndi voliyumu (V) zimagwirizana ndi kutentha kwathunthu (T).
Mosiyana ndi zimenezi, voliyumu (V) ndi yofanana ndi kupanikizika (P).
Chiŵerengero cha 4 chimasinthidwa kukhala equation:
Zambiri:
P1 = kupanikizika koyambirira (Pa kapena N/m2)
P2 = kupanikizika komaliza (Pa kapena N/m2)
V1 = voliyumu yoyambirira (m3)
V2 = voliyumu yomaliza (m3)
T1 = kutentha koyambirira (K)
T2 = kutentha komaliza (K)
(Pa = pascal, N = Newton, m2 = mita imodzi, m3 = mamita a kiyubiki, K = Kelvin)
Ubale pakati pa kulemera kwa mpweya (m) ndi voliyumu (V)
Baluni ya mpweya wotentha ikadzazidwa, mpweya wochuluka umalowa, umakula kwambiri. Mwa kuyankhula kwina, kulemera kwa mpweya kumakhala kwakukulu, ndipo voliyumu ya baluni imakulanso kwambiri. Tikhoza kunena kuti kulemera kwa mpweya (m) kumagwirizana mwachindunji ndi voliyumu ya mpweya (V). Mwa masamu:
V ∝ m → Chiŵerengero 5
Ngati equation 4 iphatikizidwa ndi equation 5 ndiye kuti:
PV ∝ mT → Kuyerekeza 6
Chiwerengero cha ma moles (n)
Mole imodzi = kulemera kwa chinthu chomwe chili chofanana ndi kulemera kwa molekyulu ya chinthucho. Kulemera kwa molekyulu ndi kulemera kwake ndi zosiyana.
Chitsanzo 1, kuchuluka kwa molekyulu ya mpweya wa okosijeni (O2)2) = 16 u + 16 u = 32 u (molekyulu iliyonse ya okosijeni ili ndi maatomu awiri a okosijeni, pomwe atomu iliyonse ya okosijeni ili ndi kulemera kwa ma u 16). Chifukwa chake, mole imodzi O2 ili ndi kulemera kwa magalamu 32. Kapena kulemera kwa molekyulu ya O2 = 32 magalamu/mol = 32 kg/kmol.
Chitsanzo chachiwiri, molekyulu ya mpweya wa carbon monoxide (CO) = 12 u + 16 u = 28 u (molekyulu iliyonse ya carbon monoxide ili ndi atomu imodzi ya kaboni (C) ndi atomu imodzi ya okosijeni (O). Kulemera kwa atomu imodzi ya kaboni = 12 u ndi kulemera kwa atomu imodzi ya okosijeni = 16 u. 12 u + 16 u = 28 u). Motero, mole imodzi ya CO ili ndi kulemera kwa magalamu 28. Kapena kulemera kwa molekyulu ya CO = 28 magalamu/mol = 28 kg/kmol.
Chitsanzo 3, kuchuluka kwa molekyulu ya mpweya wa carbon dioxide (CO2)2) = [12 u + (2 x 16 u)] = [12 u + 32 u] = 44 u (molekyulu iliyonse ya carbon dioxide ili ndi atomu imodzi ya kaboni (C ) ndi maatomu awiri a okosijeni (O). Kulemera kwa atomu imodzi ya kaboni = 12 u ndi kulemera kwa atomu imodzi ya okosijeni = 16 u). Motero, 1 mol CO2 ili ndi kulemera kwa magalamu 44. Kapena kulemera kwa molekyulu ya CO22 = 44 magalamu/mol = 44 kg/kmol.
Chiwerengero cha ma moles (n) a chinthu = chiŵerengero cha kulemera kwa chinthucho ndi kulemera kwake kwa ma molecular. Mwa masamu, yalembedwa motere:
Chitsanzo 1: Werengani chiwerengero cha ma moles mu magalamu 64 a O2
Misa O2 = 64g
Chitsanzo 2: Werengani chiwerengero cha ma moles mu magalamu 280 a CO2
Kulemera kwa CO = 280 magalamu
Chitsanzo 3: Werengani chiwerengero cha ma moles mu magalamu 176 a CO22
Unyinji wa CO2 = 176g
Mpweya wokhazikika wa Universal (R)
Kutengera kafukufuku wochitidwa ndi asayansi, zidapezeka kuti pamene chiwerengero cha ma moles (n) chikugwiritsidwa ntchito kufotokozera kukula kwa chinthu, chiŵerengero cha proportionality cha mpweya uliwonse chimakhala ndi mtengo wofanana. Chiŵerengero cha proportionality chomwe chikukambidwa ndi chiŵerengero cha mpweya chapadziko lonse (R).
R = 8,315 J/mol.K
= 8315 kJ/kmol.K
= 0,0821 (L.atm) / (mol.K)
= 1,99 cal / mol. K
(J = Joule, K = Kelvin, L = lita, atm = mlengalenga, cal = kalori)
LAMULO LABWINO LA GASI (mu ma moles)
Kuyerekeza komwe kwatchulidwa pamwambapa kungasinthidwe kukhala equation polemba chiwerengero cha moles (n) ndi Universal Gas Constant (R).
PV = nRT
Equation iyi imatchedwa lamulo labwino la mpweya kapena equation yabwino ya mpweya ya boma.
Zambiri:
P = mpweya woipa (N/m2)2)
V = kuchuluka kwa mpweya (m3)
n = chiwerengero cha ma moles (mol)
R = mpweya wokhazikika padziko lonse lapansi (R = 8,315 J/mol.K)
T = kutentha kwathunthu kwa mpweya (K)
Pothetsa mavuto, mudzakumana ndi mawu akuti STP. STP ndi chidule cha Kutentha ndi Kupanikizika Kwabwino kapena Kutentha ndi Kupanikizika Kwabwinobwino.
Kutentha kokhazikika (T) = 0 oC = 273 K
Kupanikizika kwachizolowezi (P) = 1 atm = 1,013 x 105 N / m2 = 1,013x10 pa2 kPa = 101 kPa
Pothetsa mavuto okhudza malamulo a mpweya, kutentha kuyenera kufotokozedwa pa sikelo ya Kelvin (K).
Ngati mpweya ukupitirirabe kukhala woyezera, choyamba usinthe kukhala mpweya wokwanira.
Kupanikizika kotheratu = kuthamanga kwa mpweya + kuthamanga kwa gauge (kuthamanga kwa mpweya = kuthamanga kwa mpweya wakunja)
Ngati chomwe chikudziwika ndi kuthamanga kwa mpweya (palibe kuthamanga kwa mpweya), thetsani vutoli mwachindunji.
Chitsanzo cha funso 1:
Pakupanikizika kwa mpweya wa carbon dioxide (101 kPa), kutentha kwa mpweya wa carbon dioxide = 20 oC ndi voliyumu = malita awiri. Ngati kupanikizika kwasinthidwa kufika pa 201 kPa ndipo kutentha kwawonjezeka kufika pa 40 oC, werengerani kuchuluka komaliza kwa mpweya wa carbon dioxide.
Zokambirana
Amadziwika kuti:
P1 = 101 kPa
P2 = 201 kPa
T1 = 20 oC + 273 K = 293 K
T2 = 40 oC + 273 K = 313 K
V1 = 2 lita
Anafunsa: V2
Yankho:
Chitsanzo cha funso 2:
Dziwani kuchuluka kwa ma mole awiri a mpweya pa STP (ganizirani kuti mpweya uwu ndi mpweya wabwino kwambiri)
Zokambirana
Kuchuluka kwa ma mole awiri a mpweya pa STP (kutentha ndi kupanikizika kokhazikika) ndi malita 44,8.
Chitsanzo cha funso 3:
Kuchuluka kwa mpweya wa okosijeni pa STP = 20 m3Kodi mpweya wa okosijeni ndi wolemera bwanji?
Zokambirana
Kulemera kwa molekyulu ya mpweya = 32 magalamu/mol (kulemera kwa mole imodzi ya mpweya = 32 magalamu). Motero, kulemera kwa mpweya wa mpweya ndi:
kulemera (m) = chiwerengero cha ma molekyulu (n) x kulemera kwa ma molekyulu
kulemera = (ma moles 893) x (32 magalamu/mol) = 28576 magalamu = 28,576 kg
Chitsanzo cha funso 4:
Thanki ili ndi malita 4 a mpweya wa okosijeni (O2)2). Kutentha kwa mpweya wa okosijeni = 20 oC ndi kupanikizika komwe kunayesedwa = 20 x 105 N / m2Dziwani kulemera kwa mpweya wa okosijeni (molekyulu ya okosijeni = 32 kg/kmol = 32 magalamu/mol)
Zokambirana
LAMULO LABWINO LA GESI (M'chiwerengero cha mamolekyulu)
Ngati tisonyeza kukula kwa chinthu osati potengera kulemera (m), koma potengera kuchuluka kwa ma moles (n), ndiye kuti mpweya wokhazikika (R) umagwiritsidwa ntchito pa mpweya wonse. Izi zidapezeka koyamba ndi Amedeo Avogadro (1776-1856), wasayansi waku Italy.
Avogadro anati pamene kuchuluka, kuthamanga ndi kutentha kwa mpweya uliwonse kuli kofanana, ndiye kuti mpweya uliwonse umakhala ndi mamolekyu ofanana.
Chiganizo cholembedwa mokweza kwambiri chimatchedwa lingaliro la Avogadro. Lingaliro la Avogadro, kapena lingaliro, likugwirizana ndi mfundo yakuti R yokhazikika ndi yofanana pa mpweya wonse. Nazi umboni wina:
Choyamba, ngati tithetsa vutoli pogwiritsa ntchito equation yoyenera ya gas law (PV = nRT), tidzapeza kuti pamene chiwerengero cha ma moles (n) chili chofanana, kuthamanga ndi kutentha nazonso ndizofanana, ndiye kuti kuchuluka kwa mpweya wonse kudzakhala kofanana, ngati tigwiritsa ntchito gas constant (R = 8,315 J/mol.K). Pa STP, mpweya uliwonse womwe uli ndi ma moles ofanana (n) udzakhala ndi voliyumu yofanana. Voliyumu ya mole imodzi ya mpweya pa STP = malita 22,4. Voliyumu ya ma moles awiri a mpweya = malita 44,8. Voliyumu ya ma moles atatu a mpweya = malita 67,2. Ndi zina zotero… izi zikugwira ntchito pa mpweya wonse.
Chachiwiri, chiwerengero cha mamolekyu mu mole imodzi ndi chimodzimodzi pa mpweya wonse. Chiwerengero cha mamolekyu mu mole imodzi = chiwerengero cha mamolekyu pa mole = nambala ya Avogadro (N)A). Kotero chiwerengero cha Avogadro ndi chimodzimodzi pa mpweya wonse.
Kukula kwa nambala ya Avogadro kumapezeka kudzera mu miyeso:
NA = 6,02 x 1023 mamolekyulu/mol
Kuti tipeze chiwerengero chonse cha mamolekyu (N), tikhoza kuchulukitsa chiwerengero cha mamolekyu pa mole (NA) ndi chiwerengero cha mamolekyu (n).
Iyi ndiyo njira yabwino kwambiri yowerengera kuchuluka kwa mamolekyulu a mpweya.
Zambiri:
P = Kupanikizika
V = Voliyumu
N = Chiwerengero chonse cha mamolekyulu
k = chosasintha cha Boltzmann (k = 1,38 x 1023 J/K)
T = Kutentha
Volume
Lita imodzi (L) = 1000 milliliters (mL) = 1000 cubic centimeters (cm)3)
Lita imodzi (L) = 1 kiyubiki decimeter (dm)3) = 1 x 103 m3
Kupanikizika
1 N/m2 = 1 Pa
1 atm = 1.013 x 105 N / m2 = 1,013x10 pa5 Pa = 1,013 x 102 kPa = 101,3 kPa (nthawi zambiri 101 kPa imagwiritsidwa ntchito)
Pa = pascal
atm = mlengalenga
Mphamvu yamkati ya mpweya wabwino kwambiri
Mphamvu yamkati ya mpweya wabwino wa monatomic
Mphamvu yamkati ya mpweya wabwino wa monatomic ndi chiwerengero chonse cha mphamvu ya kinetic yosinthika ya mamolekyulu a mpweya wabwino wa monatomic. Chiwerengero chonse cha mphamvu ya kinetic yosinthika ya mamolekyulu a mpweya wabwino = chopangidwa ndi mphamvu yapakati ya kinetic yosinthika ya molekyulu iliyonse ndi chiwerengero cha mamolekyulu (N). Mwa masamu:
Zambiri:
U = Mphamvu yamkati ya mpweya wabwino wa monatomic (J)
N = Chiwerengero cha mamolekyulu
k = chosasintha cha Boltzmann (k = 1,38 x 10 23 J/K)
T = Kutentha konse (K)
n = Chiwerengero cha ma moles (mol)
R = Mpweya wosasinthika (R = 8,315 J/mol.K = 8315 kJ/kmol.K)
Mphamvu mu mpweya wabwino wa diatomic
Mphamvu yamkati ya mpweya wabwino wa diatomic ndi kuchuluka kwa mphamvu ya kinetic yosinthika, mphamvu ya kinetic yozungulira, ndi mphamvu ya kinetic yogwedezeka ya mamolekyu a mpweya wabwino wa diatomic. Malinga ndi mfundo ya equipartition of energy, mphamvu yamkati ya mpweya wabwino wa diatomic ndi:
U = 5/2 n RT
Mphamvu mu mpweya wabwino wa polyatomic
Mphamvu yamkati ya mpweya wabwino wa polyatomic ndi kuchuluka kwa mphamvu ya kinetic yosinthika, mphamvu ya kinetic yozungulira, ndi mphamvu ya kinetic yogwedezeka ya mamolekyu a mpweya wabwino wa polyatomic. Malinga ndi mfundo ya equipartition of energy, mphamvu yamkati ya mpweya wabwino wa polyatomic ndi:
U = 7/2 n RT
Mphamvu mu mpweya weniweni
Mphamvu zomwe zili mu mpweya weniweni zimadaliranso kutentha. Pamene mpweya weniweni uli wokwera mokwanira (voliyumu ya mpweya weniweni ndi yochepa), mpweya weniweni umayamba kusonyeza khalidwe losasinthasintha. Chifukwa chake, tinganene kuti mphamvu zomwe zili mu mpweya weniweni zimadaliranso kupanikizika ndi kuchuluka kwake.
