Question

Two perfect gases one is monoatomic and another diatomic at absolute temperatures T₁ and T₂ are mixed. There is no loss of energy. The temperature of mixture, if masses of molecules are m₁ and m₂ and the number of molecules in the gases are n₁ and n₂ respectively –

• A. $\frac{T_{1} + T_{2}}{2}$
• B. $\frac{5n_{1}T_{1} + 3n_{2}T_{2}}{5n_{1} + 3n_{2}}$
• C. $\frac{3n_{1}T_{1} + 5n_{2}T_{2}}{3n_{1} + 5n_{2}}$
• D. $\sqrt{T_{1}T_{2}}$

Answer 1

Answer: (C)

$\frac{3n_{1}T_{1} + 5n_{2}T_{2}}{3n_{1} + 5n_{2}}$

Answer 2

$n_{1}\left( \frac{3}{2}KT_{1} \right) + n_{2}\left( \frac{5}{2}KT_{2} \right) = n_{1}\left( \frac{3}{2}KT^{'} \right) + n_{2}\left( \frac{5}{2}KT^{'} \right)$

$\frac{3n_{1}T_{1} + 5n_{2}T_{2}}{3n_{1} + 5n_{2}} = T'$