Three perfect gases at absolute temperatures `T_1, T_2` and `T_3` are mixed. The masses of molecules are `m_1, m_2` and `m_3` and the number of molecules are `n_1, n_2` and `n_3` respectively. Assuming no loss of energy, then final temperature of the mixture is :

Options

A. `(n_(1)T_(1)^(2) + n_(2)T_(2)^(2) + n_(3)T_(3)^(2))/(n_(1)T_(1) + n_(2)T_(2) + n_(3)T_(3))`
B. `(n_(1)^(2)T_(1)^(2) + n_(2)^(2)T_(2)^(2) + n_(3)^(2)T_(3)^(2))/(n_(1)T_(1) + n_(2)T_(2) + n_(3)T_(3))`
C. `(T_(1) + T_(2) + T_(3))/(3)`
D. `(n_(1)T_(1) + n_(2)T_(2) + n_(3)T_(3))/(n_(1) + n_(2) + n_(3))`

Answer

D

Explanation

`(n_(1)C_(V_(1))T_(1) = n_(2)C_(V_(2))C_(V_(2))T_(2) + n_(3)C_(V_(3))T_(3))`
=`(n_(1)+n_(2) +n_(3))C_(V_("mtx"))T`
As `C_(V_(1)) = C_(V_(2))"so" T = (n_(1)T_(1)+n_(2)T_(2)+n_(3)T_(3))/(n_(1)+n_(2) +n_(3))`