Three perfect gases at absolute temperature T1, T2 and T3 are mixed. The masses of molecules are m1,m2 and m3 and the number of molecules is n1,n2 and n3 respectively.Assuming no loss of energy, the final temperature of the mixture is - Zigya
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Three perfect gases at absolute temperature T1, T2 and T3 are mixed. The masses of molecules are m1,m2 and m3 and the number of molecules is n1,n2 and n3 respectively.Assuming no loss of energy, the final temperature of the mixture is

  • fraction numerator straight n subscript 1 straight T subscript 1 plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 over denominator straight n subscript 1 plus space straight n subscript 2 plus space straight n subscript 3 end fraction
  • fraction numerator straight n subscript 1 straight T subscript 1 superscript 2 space plus straight n subscript 2 straight T subscript 2 superscript 2 space plus straight n subscript 3 straight T subscript 3 superscript 2 over denominator straight n subscript 1 straight T subscript 1 space plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 end fraction
  • fraction numerator straight n squared subscript 1 straight T subscript 1 superscript 2 space plus straight n squared subscript 2 straight T subscript 2 superscript 2 space plus straight n squared subscript 3 straight T subscript 3 superscript 2 over denominator straight n subscript 1 straight T subscript 1 space plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 end fraction
  • fraction numerator straight n squared subscript 1 straight T subscript 1 superscript 2 space plus straight n squared subscript 2 straight T subscript 2 superscript 2 space plus straight n squared subscript 3 straight T subscript 3 superscript 2 over denominator straight n subscript 1 straight T subscript 1 space plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 end fraction


A.

fraction numerator straight n subscript 1 straight T subscript 1 plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 over denominator straight n subscript 1 plus space straight n subscript 2 plus space straight n subscript 3 end fraction

For adiabatic process i.e., no heat change

straight F over 2 straight n subscript 1 straight k subscript 1 straight T subscript 1 space plus fraction numerator begin display style straight F end style over denominator begin display style 2 end style end fraction straight n subscript 2 kT subscript 2 space plus fraction numerator begin display style straight F end style over denominator begin display style 2 end style end fraction straight n subscript 3 kT subscript 3 space
equals fraction numerator begin display style straight F end style over denominator begin display style 2 end style end fraction left parenthesis straight n subscript 1 plus straight n subscript 2 plus straight n subscript 3 right parenthesis kT
rightwards double arrow space straight T space equals space fraction numerator straight n subscript 1 straight T subscript 1 space plus straight n subscript 2 straight T subscript 2 plus straight n subscript 3 straight T subscript 3 over denominator space straight n subscript 1 plus straight n subscript 2 plus straight n subscript 3 end fraction

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