Mullid

Ülesanne. Kui palju energiat kulub puhumaks seebimulli läbimõõduga 8 space c m temperatuuril 20 space degree C ? Kui suure läbimõõduga mulli saaks samal temperatuuril sama energiakogusega puhuda petrooleumist?

Lahendus. Paneme kirja andmed.

Antud:
d subscript s equals 8 space c m equals 8 times 10 to the power of negative 2 space end exponent m alpha subscript s equals 4 comma 5 times 10 to the power of negative 2 end exponent space J over m squared alpha subscript p equals 2 comma 4 times 10 to the power of negative 2 end exponent space J over m squared minus negative negative negative negative negative negative negative negative negative negative A equals ? d subscript p equals ?

Andmetes oleme kirja pannud seebilahuse ning petrooleumi pindpinevustegurid (vastavalt alpha subscript s ja alpha subscript p) temperatuuril 20 space degree C. Paneme kirja seebimulli pinna pindala valemi

S subscript s equals 2 times 4 times pi times open parentheses d subscript s over 2 close parentheses squared comma

kus kordaja 2 arvestab, et mullil on nii seesmine kui väline pind. Nüüd võimegi arvutada töö, mis tuleb teha seebimulli moodustamiseks molekulidevaheliste jõudude vastu:

A equals alpha subscript s S subscript s equals 4 comma 5 times 10 to the power of negative 2 end exponent space J over m squared times 2 times 4 times pi times open parentheses fraction numerator 8 times 10 to the power of negative 2 end exponent space m over denominator 2 end fraction close parentheses squared equals 1.8 times 10 to the power of negative 3 space space end exponent J.

Rehkendamaks kui suure läbimõõduga petrooleumimulli sama energiaga saame moodustada paneme kirja analoogse valemi petrooleumi kohta

A equals alpha subscript p S subscript p equals alpha subscript p times 2 times 4 times pi times open parentheses d subscript p over 2 close parentheses squared comma

millest avaldame petrooleumimulli diameetri:d subscript p equals square root of fraction numerator A over denominator alpha subscript p times 2 times pi end fraction end root equals square root of fraction numerator 1 comma 8 times 10 to the power of negative 3 end exponent space J over denominator 2 comma 4 times 10 to the power of negative 2 end exponent space J over m squared times 2 times pi end fraction end root equals 1 comma 1 times 10 to the power of negative 1 end exponent space m equals space 11 space c m.

VASTUS: seebimulli puhumiseks kulub energiat 1.8 times 10 to the power of negative 3 space space end exponent J comma millega saaks moodustada petrooleumimulli läbimõõduga 11 space c m.