Question

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

$fraction numerator straight n subscript 1 straight T subscript 1 plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 over denominator straight n subscript 1 plus space straight n subscript 2 plus space straight n subscript 3 end fraction$
$fraction numerator straight n subscript 1 straight T subscript 1 superscript 2 space plus straight n subscript 2 straight T subscript 2 superscript 2 space plus straight n subscript 3 straight T subscript 3 superscript 2 over denominator straight n subscript 1 straight T subscript 1 space plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 end fraction$
$fraction numerator straight n squared subscript 1 straight T subscript 1 superscript 2 space plus straight n squared subscript 2 straight T subscript 2 superscript 2 space plus straight n squared subscript 3 straight T subscript 3 superscript 2 over denominator straight n subscript 1 straight T subscript 1 space plus straight n subscript 2 straight T subscript 2 space plus straight n subscript 3 straight T subscript 3 end fraction$
$fraction numerator open parentheses straight T subscript 1 plus straight T subscript 2 plus straight T subscript 3 close parentheses over denominator 3 end fraction$

Solution

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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Mechanical Properties Of Fluids

Some More Questions From Mechanical Properties of Fluids Chapter

Define Dulong and Pettit’s law of specific heat.

Who explained the correct variation of specific heat with temperature in the lower range of temperature?

What is the SI unit of molar specific heat?

Define heat capacity.

What are the units of heat capacity?

Define Dulong and Pettit’s law of specific heat.

Who explained the correct variation of specific heat with temperature in the lower range of temperature?

Do the gases have only one value of specific heat?

What is thermometry?

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Mechanical Properties Of Fluids

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

Some More Questions From Mechanical Properties of Fluids Chapter

Define Dulong and Pettit’s law of specific heat.

Who explained the correct variation of specific heat with temperature in the lower range of temperature?

What is the SI unit of molar specific heat?

Define heat capacity.

What are the units of heat capacity?

Define Dulong and Pettit’s law of specific heat.

Who explained the correct variation of specific heat with temperature in the lower range of temperature?

Do the gases have only one value of specific heat?

What is thermometry?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation