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Suatu gas ideal dimampatkan secara adiabatik sehin...

Suatu gas ideal dimampatkan secara adiabatik begin mathsize 14px style open parentheses gamma equals 1 comma 4 close parentheses end style sehingga volumenya menjadi begin mathsize 14px style 3 over 4 end style volume awal. Tentukan usaha yang dibutuhkan jika tekanan dan volume awalnya berturut-turut begin mathsize 14px style 1 space bar space left parenthesis 1 space bar equals 1 cross times 10 to the power of 5 space Pa right parenthesis end style dan begin mathsize 14px style 1 space straight m cubed end style!

Jawaban:

Diketahui,

gamma equals 1 comma 4 V subscript 2 equals 3 over 4 V subscript 1 P subscript 1 equals 1 space bar equals 1 cross times 10 to the power of 5 space Pa V subscript 1 equals 1 space straight m cubed

Ditanya,

W=...?

Jawab,

Adiabatik adalah proses keadaan termodinamika tanpa adanya perpindahan kalor.

Dengan menggunakan persamaan proses gas diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell P subscript 1 V subscript 1 to the power of gamma end cell equals cell P subscript 2 V subscript 2 to the power of gamma end cell row cell open parentheses V subscript 1 over V subscript 2 close parentheses to the power of gamma end cell equals cell P subscript 2 over P subscript 1 end cell row cell open parentheses fraction numerator up diagonal strike V subscript 1 end strike over denominator begin display style 3 over 4 up diagonal strike V subscript 1 end strike end style end fraction close parentheses to the power of 1 comma 4 end exponent end cell equals cell P subscript 2 over P subscript 1 end cell row cell P subscript 2 over P subscript 1 end cell equals cell open parentheses 4 over 3 close parentheses to the power of 1 comma 4 end exponent end cell row cell space P subscript 2 over P subscript 1 end cell equals cell 1 comma 495 end cell row cell P subscript 2 end cell equals cell 1 comma 495. P subscript 1 end cell row blank equals cell 1 comma 495 cross times 10 to the power of 5 space P a end cell end table

Dengan menggunakan persamaan usaha pada proses adiabatik diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row W equals cell fraction numerator 1 over denominator gamma minus 1 end fraction open parentheses P subscript 1 V subscript 1 minus P subscript 2 V subscript 2 close parentheses end cell row blank equals cell fraction numerator 1 over denominator 1 comma 4 minus 1 end fraction open parentheses 10 to the power of 5 cross times 1 minus 1 comma 495 cross times 10 to the power of 5 cross times 3 over 4 close parentheses end cell row blank equals cell fraction numerator 1 over denominator 0 comma 4 end fraction cross times left parenthesis negative 0 comma 12125 right parenthesis cross times 10 to the power of 5 end cell row blank equals cell negative 0 comma 303125 cross times 10 to the power of 5 space straight J end cell end table 

Jadi, usaha yang dibutuhkan gas ideal tersebut adalah Error converting from MathML to accessible text..

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