Õhu molaarmass

Ülesanne. Õhu tiheduseks temperatuuril_{$300 space K$}ja rõhul_{$103 space k P a$}mõõdeti_{$1 comma 2 space fraction numerator k g over denominator m cubed end fraction.$}Leia nende mõõtmistulemuste põhjal õhu molaarmass.

Lahendus. Paneme kirja andmed.

Antud:
$T equals 300 space K equals 3 times 10 squared space K p equals 103 space k P a equals 1.03 times 10 to the power of 5 space P a rho equals 1 comma 2 space fraction numerator k g over denominator m cubed end fraction R equals 8 comma 31 space fraction numerator J over denominator m o l times K end fraction minus negative negative negative negative negative negative negative negative negative negative negative negative negative negative M equals ?$

Lahendame ülesande eeldusel, et õhk on ideaalne gaas ning rahuldab olekuvõrrandit

$p equals fraction numerator rho R T over denominator M end fraction comma$

kus_$p$on õhu rõhk,_$rho$on õhu tihedus, _$T$on õhu temperatuur, _$R$on universaalne gaasikonstant ning_$M$on õhu molaarmass. Viimane meid huvitabki, seepärast avaldame

$M equals fraction numerator rho R T over denominator p end fraction$

ning arvutame

$M equals fraction numerator 1 comma 2 space fraction numerator k g over denominator m cubed end fraction times 8 comma 31 space fraction numerator J over denominator m o l times K end fraction times 3 times 10 squared space K over denominator 1.03 times 10 to the power of 5 space P a end fraction equals 29 times 10 to the power of negative 3 end exponent space fraction numerator k g over denominator m o l end fraction equals 29 space fraction numerator g over denominator m o l end fraction.$

VASTUS: õhu molaarmass on_{$29 space fraction numerator g over denominator m o l end fraction.$}