Question

Two perfect gases at absolute temperatures $T_{1}$ and $T_{2}$ are mixed. There is no loss of energy. The masses of the molecules are $m_{1}$ and $m_{2}$. The number of mole in the gases are $n_{1}$ and $n_{2}$. The temperature of the mixture is

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

Answer 1

Answer: (C)

As there is no loss of energy,
$\Delta U_{1}+\Delta U_{2}=0$
$n_{1} C_{\nu}\left(T-T_{1}\right)+n_{2} C_{\nu}\left(T-T_{2}\right)=0$
$C_{V}=$ Specific heat at constant volume.
$\Rightarrow n_{1} T+n_{2} T=n_{1} T_{1}+n_{2} T_{2}$
or $T=\left(\frac{n_{1} T_{1}+n_{2} T_{2}}{n_{1}+n_{2}}\right)$.