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Question

Two perfect gases at absolute temperatures T1 and T2 are mixed. Assuming that there is no loss of energy. Find the temperature T of the mixture if the masses of the molecules are m1 and m1 and the number of molecules in the gases are n1 and n2.


A

T1T2

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B

T1T2

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C

n1T1 + n2T2n1 + n2

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D

n1T1 + n2T2T1 + T2

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Solution

The correct option is C

n1T1 + n2T2n1 + n2


According to the kinetic theory of gases, the kinetic energy of an ideal gas molecule at temperature T is given by K.E = 32kT. As there is no force of attraction among the molecules of a perfect gas, PE. of the molecules is zero. So the energy of a molecule of a perfect gas is as follows:

E = K.E. + P.E. = 32kT + 0 = 32kT

Now, if T is the temperature of the mixture , by conservation of energy , we have

n1E1 + n2E2 = (n1+n2)E

or

n1(32 kT1) + n2(32 kT2) = (n1 + n2) 32kT T=n1T1+n2T2n1 + n2


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