Zitsanzo 19 za Chiphunzitso cha Kinetic cha Mpweya
1. Mpweya wabwino kwambiri mu chidebe chotsekedwa poyamba umakhala ndi mphamvu ya P ndi voliyumu V. Ngati mphamvu ya mpweya yawonjezeka kufika ku nthawi 4 kuposa yoyamba ndipo mphamvu ya mpweya imakhalabe yofanana, chiŵerengero cha mphamvu yoyamba ya kinetic ndi mphamvu yomaliza ya kinetic ya mpweya ndi...
Zokambirana
Ndizodziwika kuti :
Kupanikizika koyamba (P)1) = P
Kupanikizika komaliza (P)2) = 4P
Voliyumu yoyamba (V)1) = V
Voliyumu yomaliza (V)2) = V
Anafunsa Kuyerekeza mphamvu yoyambirira ya kinetic ndi mphamvu yomaliza ya kinetic (EK)1 : EK2)
Yankhani :
Ubale pakati pa kupanikizika (P), voliyumu (V) ndi mphamvu ya kinetic (EK) ya mpweya wabwino :
Kuyerekeza mphamvu yoyambirira ya kinetic ndi mphamvu yomaliza ya kinetic :
2. Dziwani mphamvu yapakati ya kinetic ya mamolekyu a mpweya pa kutentha kwa madigiri 57oC!
Zokambirana
Ndizodziwika kuti :
Kutentha kwa mpweya (T) = 57oC + 273 = 330 Kelvin
Chosasintha cha Boltzmann (k) = 1,38 x 10-23 Joule/Kelvin
Anafunsa : Mphamvu yapakati ya kinetic yomasulira
Yankhani :
Ubale pakati pa mphamvu ya kinetic ndi kutentha kwa mpweya :
Mphamvu yapakati ya kinetic yomasulira :
3. Mpweya pa kutentha kwa madigiri 27oC ili mu chidebe chotsekedwa. Kuti mphamvu yake ya kinetic iwonjezere kuwirikiza kawiri mphamvu yake yoyambirira ya kinetic, mpweya uyenera kutenthedwa kufika pa kutentha kwa...
Zokambirana
Ndizodziwika kuti :
Kutentha koyambirira (T)1= = 27oC + 273 = 300 K
Mphamvu yoyambirira ya kinetic = EK
Mphamvu yomaliza ya kinetic = 4 EK
Anafunsa Kutentha komaliza (T)2)
Yankhani :
Kutentha komaliza kwa mpweya ndi 600 K kapena 327oC.
4. Mpweya wabwino uli pamalo otsekedwa. Mpweya wabwino umatenthedwa mpaka liwiro lapakati la tinthu ta mpweya litakwera kufika katatu kuposa liwiro loyamba. Ngati kutentha koyambirira kwa mpweya kuli madigiri 27.oC, ndiye kutentha komaliza kwa mpweya woyenera ndi...
Zokambirana
Ndizodziwika kuti :
Kutentha koyambirira = 27oC + 273 = 300 Kelvin
Liwiro loyambirira = v
Liwiro lomaliza = 2v
Anafunsa : Kutentha komaliza kwa mpweya wabwino
Yankhani :
Liwiro lapakati lomaliza = 2 x Liwiro lapakati loyambirira
5. Ma mole atatu a mpweya ali m'chipinda chokhala ndi voliyumu ya malita 36. Molekyu iliyonse ya mpweya ili ndi mphamvu ya kinetic ya 5 x 10-21 Joule. Mpweya wosasinthika = 8,315 J/mol.K ndi Boltzmann wosasinthika = 1,38 x 10-23 J/K. Werengani kuchuluka kwa mpweya m'chipindamo!
Zokambirana
Ndizodziwika kuti :
Chiwerengero cha ma moles (n) = 3 mol
Kuchuluka kwa madzi = malita 36 = 36 dm3 = 36 x 10-3 m3
Chosasintha cha Boltzmann (k) = 1,38 x 10-23 J/K
Mphamvu ya kinetic (EK) = 5 x 10-21 Joule
Mpweya wosasinthika wa Universal (R) = 8,315 J/mol.K
Anafunsa : mpweya woipa (P)
Yankhani :
Werengerani kutentha (T) pogwiritsa ntchito njira ya mphamvu ya kinetic ya mpweya ndi kutentha:
Werengerani kuthamanga kwa mpweya pogwiritsa ntchito njira ya Ideal Gas Law (mu chiwerengero cha ma moles, n):
Mpweya wothamanga ndi 1,67 x 10 5 Pascal kapena 1,67 atmospheres.
6. Mu chotengera chotsekedwa, kuchuluka kwa mpweya kumawonjezeka kufika kawiri kuposa kuchuluka koyambirira (V)o = voliyumu yoyambirira, Po = kupanikizika koyambirira) ndipo kutentha kwa mpweya kumawonjezeka kufika ku nthawi 4 kuposa koyambirira. Kupanikizika kwa mpweya kumakhala...
A. Po
B. 2 Po
C. 4 Po
D. 6 Po
E. 8 Po
Zokambirana
Amadziwika kuti:
Kuchuluka koyambirira kwa mpweya (V)1) = Vo
Kuchuluka komaliza kwa mpweya (V)2) = 2Vo
Kutentha koyambirira kwa mpweya (T)1) = T
Kutentha komaliza kwa mpweya (T)2) = 4T
Kuthamanga kwa mpweya koyambirira (P)1) = Po
Anafunsa kuti: Kupanikizika kwa mpweya komaliza (P)2)
Yankho:
Yankho lolondola ndi B.
7. Mpweya wabwino kwambiri umadutsa mu njira ya isothermal, kotero kuti kuthamanga kumakhala kawiri kuposa kuthamanga koyambirira, kenako voliyumu imakhala...
A. Yoyambirira kasanu ndi kamodzi
B. yoyambirira kasanu
C. Kuchulukitsa theka la choyambirira
D. ¼ nthawi yoyambirira
E. akadali
Zokambirana
Isothermic = kutentha kosalekeza
Amadziwika kuti:
Kuchuluka koyambirira kwa mpweya (V)1) = V
Kuthamanga kwa mpweya koyambirira (P)1) = P
Kupanikizika kwa mpweya komaliza (P)2) = 2P
Anafunsa kuti: Kuchuluka komaliza kwa mpweya (V)2)
Yankho:
P1 V1 =P2 V2
PV = (2P) V2
V = (2) V2
V2 = V / 2
V2 = ½ V
Yankho lolondola ndi C.
8. Mu chotengera chotsekedwa, kuchuluka kwa mpweya kumawonjezeka kufika kawiri kuposa kuchuluka koyamba (Vo = voliyumu yoyamba, Po = kupanikizika koyamba) ndipo kutentha kwa mpweya kumakwera kufika kanayi kuposa koyamba. Kupanikizika kwa mpweya kumakhala…
A. Po
B. 2 Po
C. 4 Po
D. 6 Po
E. 8 Po
Zokambirana
Ndizodziwika kuti :
Kuchuluka koyambirira kwa mpweya (V)1) = Vo
Kuchuluka komaliza kwa mpweya (V)2) = 2Vo
Kutentha koyambirira kwa mpweya (T)1) = T
Kutentha komaliza kwa mpweya (T)2) = 4T
Kuthamanga kwa mpweya koyambirira (P)1) = Po
Anafunsa : Kuthamanga kwa mpweya komaliza (P)2)
Yankhani :
Yankho lolondola ndi B.
9. Mpweya wabwino kwambiri umadutsa mu njira ya isothermal, kotero kuti kuthamanga kumakhala kawiri kuposa kuthamanga koyambirira, kenako voliyumu imakhala...
A. Yoyambirira kasanu ndi kamodzi
B. yoyambirira kasanu
C. Kuchulukitsa theka la choyambirira
D. ¼ nthawi yoyambirira
E. akadali
Zokambirana
Isothermic = kutentha kosalekeza
Ndizodziwika kuti :
Kuchuluka koyambirira kwa mpweya (V)1) = V
Kuthamanga kwa mpweya koyambirira (P)1) = P
Kupanikizika kwa mpweya komaliza (P)2) = 2P
Anafunsa : Kuchuluka komaliza kwa mpweya (V)2)
Yankhani :
P1 V1 =P2 V2
PV = (2P) V2
V = (2) V2
V2 = V / 2
V2 = ½ V
Yankho lolondola ndi C.
10. Kupanikizika kwa mpweya wabwino pamalo otsekedwa motsutsana ndi makoma a chubu kumapangidwa motere :
P = 2N / 3V EK
P = kupanikizika (Pa)
N = chiwerengero cha mamolekyu a mpweya (tinthu tating'onoting'ono)
V = kuchuluka kwa mpweya
EK = mphamvu yapakati ya kinetic ya mamolekyulu (J).
Mawu olondola okhudza njira yomwe ili pamwambapa ndi akuti…
A. Kupanikizika kwa mpweya motsutsana ndi khoma kumadalira kuchuluka kwa mamolekyu pa voliyumu iliyonse.
B. Mphamvu ya kinetic ya mpweya siidalira mphamvu ya mamolekyu omwe ali pamakoma.
C. Kuchuluka kwa mpweya mu silinda sikusintha ngati kuthamanga kwa mpweya kukusintha.
D. Chiwerengero cha mamolekyu a mpweya chimachepa, kotero mphamvu ya kinetic ya mamolekyu imawonjezeka.
E. Kuchuluka kwa mpweya kumawonjezeka, kotero kuchuluka kwa mamolekyu a mpweya kumawonjezeka.
Zokambirana
Chipindacho chimatsekedwa kotero kuti ngakhale kuthamanga kwa mpweya kumasintha, kuchuluka kwa mpweya mu chubucho sikusintha.
Yankho lolondola ndi C.
11. Kupanikizika kwa mpweya wabwino pamalo otsekedwa motsutsana ndi khoma la chubu kumapangidwa motere: P = (2N / 3V) EK. P = kupanikizika (Pa), N = chiwerengero cha mamolekyu ( tinthu tating'onoting'ono) a mpweya ndipo EK ndiye mphamvu yapakati ya mamolekyu (J). Kutengera ndi equation iyi, mawu olondola ndi...
A. Kupanikizika kwa mpweya motsutsana ndi khoma kumadalira mphamvu yapakati ya kinetic ya mamolekyu.
B. Mphamvu ya kinetic ya mpweya imadalira mphamvu ya mamolekyu omwe ali pamakoma.
C. Kutentha kwa mpweya mu chubu kudzasintha ngati kuthamanga kwa mpweya kukusintha.
D. Ngati kuchuluka kwa mamolekyu a mpweya kutsika, mphamvu ya kinetic ya mamolekyu idzachepa.
E. Ngati kuchuluka kwa mpweya kukukwera, kuthamanga kwa mpweya kudzachepa.
Zokambirana
Amadziwika kuti:
Fomula yokakamiza: P = (2N / 3V) EK
P = kupanikizika
N = chiwerengero cha mamolekyu a tinthu ta mpweya
V = kuchuluka kwa mpweya
EK = mphamvu yapakati ya kinetic
P imagwirizana mwachindunji ndi N ndi EK
P ndi yofanana ndi V
N ndi yofanana mwachindunji ndi voliyumu
N ndi yofanana ndi EK
Anafunsa: Ndi chiganizo chiti chomwe chili cholondola?
Yankho:
A ndi yolakwika chifukwa kutengera njira yomwe ili pamwambapa, kuthamanga kwa mpweya (P) kumadalira mphamvu ya kinetic, osati mphamvu ya kinetic yapakati.
B ndi yolakwika chifukwa kupanikizika kumadalira mphamvu ya kinetic ya mpweya, osati njira ina.
C ndi yolakwika chifukwa kutengera fomula yomwe ili pamwambapa, kutentha sikudalira kupanikizika.
D ndi wolakwika chifukwa N ndi yofanana ndi EK, kutanthauza kuti ngati N ndi yayikulu ndiye kuti EK ndi yayikulu.
E ndi wolondola chifukwa kupanikizika (P) kumasiyana malinga ndi voliyumu (V).
Yankho lolondola ndi E.
12. Ngati mpweya wabwino kwambiri m'chombo wapanikizika (wopanikizika), mpweyawo udzakumana ndi….
A. Kuchepa kwa liwiro la tinthu tating'onoting'ono
B. Kutsika kwa kutentha
C. Kuwonjezeka kwa kutentha
D. Kuwonjezera tinthu ta mpweya
E. Kuchepetsa tinthu ta mpweya
Zokambirana
Lamulo labwino la mpweya (mu ma moles) :
PV = nRT
Lamulo labwino la mpweya (mu chiwerengero cha mamolekyulu) :
PV = NkT
Ubale pakati pa mphamvu ya kinetic ndi kutentha kwa mpweya :
EK = 3/2 kT
Zambiri:
P = kupanikizika, V = voliyumu, T = kutentha, n = chiwerengero cha ma molekyulu, N = chiwerengero cha mamolekyulu, R = chokhazikika cha mpweya wachilengedwe, k = chokhazikika cha Boltzmann
Kutengera njira zitatu zomwe zili pamwambapa, mfundo zotsatirazi zaperekedwa:
– Ngati mpweya wapanikizika, voliyumu (V) ya mpweya imachepa.
– Ngati voliyumu (V) ya mpweya yachepa, kuthamanga (P) kwa mpweya kumawonjezeka ndipo kutentha (T) kwa mpweya kumawonjezeka.
– Chipindacho chatsekedwa (V ndi chosasintha) motero chiwerengero cha ma moles a mpweya (n) ndi chiwerengero cha tinthu ta mpweya (N) sichisintha.
– Ngati kutentha (T) kwa mpweya kukukwera, mphamvu ya kinetic (EK) ya mpweya ikukwera. Ngati mphamvu ya kinetic ya mpweya ikukwera, liwiro la tinthu ta mpweya limakwera (EK = ½ mv 2 , v = liwiro).
Yankho lolondola ndi C.
13. Kuchuluka kwa mpweya wabwino kwambiri mu chubu chotsekedwa kumatenthedwa mozungulira maso kuti kutentha kwake kukwere kufika kanayi pa kutentha kwake koyambirira. Mphamvu yapakati ya kinetic ya mamolekyu abwino kwambiri a mpweya ndi….
A. ¼ kuchulukitsa choyambirira
B. kuchulukitsa theka la choyambirira
C. Mofanana ndi kale
D. kawiri kachiwiri
E. Yoyamba kawiri
Zokambirana
Isochoric = voliyumu yosasinthasintha
Ubale pakati pa mphamvu ya kinetic yapakati (EK) ndi kutentha (T) kwa mpweya ukufotokozedwa ndi equation ili pansipa:
EK = 3/2 kT
Kufotokozera: EK = mphamvu ya kinetic, T = kutentha, 3/2 = kosasintha, k = kosasintha kwa Boltzmann.
Kutengera ndi njira iyi, zikuwoneka kuti mphamvu ya kinetic imagwirizana mwachindunji ndi kutentha. Chifukwa chake, kutentha kukakhala kwakukulu, mphamvu ya kinetic imakulanso. Ngati kutentha kukuchulukirachulukira kanayi, mphamvu ya kinetic imachulukiranso kanayi.
Yankho lolondola ndi E.
14. Mpweya wabwino kwambiri wokhala ndi mphamvu ya P ndi voliyumu V pamalo otsekedwa. Ngati mphamvu ya mpweya m'malomo yachepetsedwa kufika pa 1/4 ya yoyambirira pa voliyumu yokhazikika, ndiye kuti chiŵerengero cha mphamvu ya kinetic isanafike komanso itatha kuchepetsa mphamvu ndi…
A. 1: 4
B. 1: 2
C. 2: 1
D. 4: 1
E. 5: 1
Zokambirana
Amadziwika kuti :
Voliyumu yoyamba = V
Voliyumu yomaliza = V
Kupanikizika koyamba kwa mpweya = P
Kupanikizika komaliza kwa mpweya = ¼ P
Funso : kuyerekeza mphamvu yoyambirira ya kinetic ndi mphamvu yomaliza ya kinetic (EK 1 : EK 2 )
Yankho :
Ubale pakati pa kupanikizika (P), voliyumu (V) ndi mphamvu ya kinetic (EK) ya mpweya:
Kuyerekeza mphamvu yoyambirira ya kinetic ndi mphamvu yomaliza ya kinetic:
Yankho lolondola ndi D.
15. Kutentha kwa mpweya wabwino kwambiri mu chubu kumapangidwa ngati EK = 3/2 kT, pomwe T imayimira kutentha kwathunthu ndipo EK = mphamvu yapakati ya kinetic ya mamolekyu a mpweya. Kutengera ndi equation yomwe ili pamwambapa…
A. Kutentha kwa mpweya kukakhala kwakukulu, mphamvu yake ya kinetic imachepa.
B. Kutentha kwa mpweya kukakwera, tinthu ta mpweya timayenda pang'onopang'ono.
C. Kutentha kwa mpweya kukakwera, tinthu ta mpweya timayenda mofulumira.
D. Kutentha kwa mpweya kumasiyana malinga ndi mphamvu ya kinetic ya mpweya
E. Kutentha kwa mpweya sikukhudza kayendedwe ka tinthu ta mpweya.
Zokambirana
Kutengera ndi njira yomwe ili pamwambapa, kutentha kumayenderana mwachindunji ndi mphamvu ya kinetic. Kutentha kukakhala kwakukulu, mphamvu ya kinetic imakulirakulira. Mphamvu ya kinetic imayenderana ndi liwiro la kayendedwe ka tinthu ta mpweya (EK = ½ mv 2 , pomwe EK = mphamvu ya kinetic, v = liwiro). Mphamvu ya kinetic ikakulirakulira, kayendedwe ka tinthu ta mpweya kamafulumira.
Yankho lolondola ndi C.
7. Zinthu zomwe zimakhudza mphamvu ya kinetic ya mpweya pamalo otsekedwa:
(1) kupanikizika
(2) voliyumu
(3) kutentha
(4) mitundu ya zinthu
Chiganizo cholondola ndi ichi….
A. (1) ndi (2)
B. (1) ndi (3)
C. (1) ndi (4)
D. (2) yokha
E. (3) yokha
Zokambirana
Malowa atsekedwa kotero kuti kuchuluka kwa mpweya kumakhala kosasintha, kuchuluka kwa mpweya sikukhudza mphamvu ya kinetic.
Yankho lolondola ndi B.
16. Samalani mawu otsatirawa!
(1) Chiwerengero cha tinthu ta mpweya chikuwonjezeka
(2) Chiwerengero cha ma moles chimachepa
(3) Kutentha kwawonjezeka
(4) Kuchuluka kwa voliyumu
Zinthu zomwe zingawonjezere kupanikizika kwa mpweya pamalo otsekedwa zikuwonetsedwa ndi chiwerengero cha…
Zokambirana
Chiyerekezo cha kuthamanga kwa mpweya pamalo otsekedwa:
Zambiri:
P = kupanikizika, N = chiwerengero cha mamolekyulu a mpweya, m = kulemera, v = liwiro lapakati la mamolekyulu, V = kuchuluka kwa chidebe, n = chiwerengero cha mamolekyulu.
Kutengera ndi equation yomwe ili pamwambapa,
Ngati kuchuluka kwa tinthu ta mpweya (N) kukukwera, kuthamanga kwa mpweya (P) kumawonjezeka.
Ngati chiwerengero cha ma moles (n) chachepa ndiye kuti kuthamanga kwa mpweya (P) kumachepa.
Ngati kutentha (T) kwawonjezeka ndiye kuti mpweya woipa (P) umawonjezeka.
Ngati voliyumu (V) ikukwera, kuthamanga kwa mpweya (P) kumachepa.
Chifukwa chake zinthu zomwe zingawonjezere kupanikizika kwa mpweya pamalo otsekedwa ndi 1 ndi 3.
17. Mpweya wa Argon umakhala m'chipinda chotsekedwa pamene kutentha kumasintha kufika pa kawiri kuposa koyambirira, kenako liwiro la kuyenda kwa tinthu ta argon limasintha kufika pa... kuchulukitsa koyambirira.
Zokambirana
Ndizodziwika kuti:
Kutentha koyambirira = T
Kutentha komaliza = 2T
Liwiro loyambirira = v
Funso: Liwiro lomaliza = ….v
Yankho:
Fomula yolumikizirana pakati pa liwiro, mphamvu yapakati ya kinetic ndi kutentha kwa mpweya:
Zambiri:
v = liwiro, k = Bolztmann nthawi zonse, T = kutentha, m = kulemera
Liwiro loyamba:
Tiyerekeze kuti k = 1, T = 1 ndi m = 1.
Ngati kutentha komaliza = 2 ndiye kuti liwiro lomaliza ndi:
Liwiro lomaliza = √ kuwirikiza kawiri kuposa loyambirira.
18. Kuchuluka kwina kwa mpweya wabwino wa monatomic poyamba kumakhala ndi kupanikizika kwa 120 kPa. Kenako, mpweyawo umatenthedwa ndi kupanikizika kosalekeza kuti ukule. Tiyerekeze kuti mpweya wokhazikika wa chilengedwe chonse umafotokozedwa ngati R J.mol -1 .K -1 . Ngati panthawiyi kutentha kwa mpweya kukukwera kufika pa 38,4/R Kelvin ndipo ntchito pa kmol iliyonse yomwe mpweyawo ukuchita kuti ukule ndi 8,4 J, ndiye kuti voliyumu yoyambirira ya mpweya pa kmol iliyonse ndi...
A. 210 cc
B. 225 cc
C. 235 cc
D. 240 cc
E. 250 cc
Zokambirana
Ndizodziwika kuti:
Kupanikizika (P) = 120 kPa = 120.000 Pascals
Mpweya wokhazikika wa chilengedwe chonse = R
Kutentha (T) = 38,4/R
Ntchito (W) pa kilomol = 8,4 Joules
Yafunsidwa: Kuchuluka koyambirira (V 1 ) pa kilomol
Yankho:
Werengerani voliyumu yomaliza (V 2 ):
PV 2 = n RT
120.000 (V 2 ) = R (38,4/R)
120.000 (V 2 ) = 38,4
V 2 = 38,4 /120.000
V 2 = 0,00032
V 2 = 0,32 x 10 -3 m 3 /kmol
V 2 = 0,32 x 10 -3 x 10 6 cm 3 / kml
V 2 = 0,32 x 10 3 cm 3 /kmol
V 2 = 320 cm 3 /kmol
V 2 = 320 cc/kmol
Werengerani voliyumu yoyambirira (V 1 ):
W = P (V 2 – V 1 )
8,4 = 120 x 10 3 (0,32 x 10 -3 – V 1 )
8,4 = 120 x 10 3 x 0,32 x 10 -3 – (120 x 10 3 V 1 )
8,4 = 120 x 0,32 – (120 x 10 3 V 1 )
8,4 = 38,4 – (120 x 10 3 V 1 )
(120 x 10 3 V 1 ) = 38,4 – 8,4
(120 x 10 3 V 1 ) = 30
V 1 = 30 / (120 x 10 3 )
V 1 = 0,25 x 10 -3 m 3
V 1 = 0,25 x 10 -3 x 10 6 cm 3
V 1 = 0,25 x 10 3 cm 3
V 1 = 250 cm 3
V 1 = 250 cc
Yankho lolondola ndi E.
19. Mpweya wa Argon ukhoza kuonedwa ngati mpweya wabwino kwambiri. Poyamba mpweyawo uli ndi mphamvu yamkati E1 ndi kutentha T1Mpweya umadutsa mu ndondomeko yogwira ntchito W, kutulutsa mphamvu yokwanira Q ndipo mkhalidwe womaliza wa mphamvu yamkati ndi E.f ndi kutentha TfKukula kwa kusintha kwa mphamvu kwawonetsedwa pachithunzi pamwambapa. Kodi mapeto a njirayi ndi otani?
A. Gasi imadutsa mu njira ya isobaric ndipo T f < T i
B. Gasi amadutsa mu ndondomeko ya adiabatic ndipo T f < T i
C. Gasi imadutsa mu njira ya isochoric ndipo T f < T i
D. Gasi imadutsa mu njira ya isothermal ndipo T f = T i
E. Gasi imadutsa mu njira ya isochoric ndipo T f = T i
Zokambirana
Kutengera ndi chithunzicho, mphamvu yoyambirira (E i ) ndi mphamvu yomaliza (E f ) sizisintha, mwa kuyankhula kwina kusintha kwa mphamvu yamkati ndi zero. Fomula ya kusintha kwa mphamvu yamkati: ΔU = 3/2 N k ΔT
Kutengera ndi njira iyi, ngati kusintha kwa mphamvu yamkati ndi zero (ΔU=0), ndiye kuti kusintha kwa kutentha ndi zero (ΔT=0). Kusintha kwa kutentha ndi zero kumatanthauza kuti kutentha sikunasinthe. Ngati kutentha sikunasinthe, mpweyawo ukuchitika mu njira ya isothermal.
Yankho lolondola ndi D.
Gwero la funso:
Mafunso a National Examination Physics a Senior High School/Vocational High School
