Question

Two perfect gases at absolute temperatures $T_1$ and $T_2$ are mixed. There is no loss of energy. The temperature of mixture of masses of molecules are $m_1$ and $m_2$ and the number of molecules in the gases are $n_1$ and $n_2$ respectively, is

• A. $\frac{ T_1 + T_2 }{ 2 }$
• B. $\frac{ n_1 T_1 + n_2T_2 }{ n_1 + n_2 }$
• C. $\frac{ n_1 T_2 + n_2T_1 }{ n_1 + n_2 }$
• D. $\sqrt{ T_1 T_2 / n_1n_2}$

Answer 1

Answer: (B)

$\frac{ n_1 T_1 + n_2T_2 }{ n_1 + n_2 }$

Answer 2

We know E = $\frac{3}{ 2} n kT$
k =Boltzmann's constant
$\therefore \frac{3}{ 2} n_1 k T_1 + \frac{3}{ 2} n_2 k T_2 = \frac{3}{ 2} (n_1 + n_2) k T$
T = $\frac{ n_1 T_1 + n_2T_2 }{ n_1 + n_2 }$