A mixture of helium $\text{(He)}$ and nitrogen ($\mathrm{N}_{2}$) expands in a turbine from $800$ $\mathrm{kPa}$ to $100$ $\mathrm{kPa}$. The mixture composition is $40\% ~\mathrm{He}$ and $60 \% \mathrm{~N}_{2}$ by mass. The turbine inlet temperature is $1000$ $\mathrm{K}$. The temperature (in $\mathrm{K}$) at the turbine exit is $\_\_\_\_$ (rounded off to two decimal places).
Assume:
The process is isentropic. Kinetic and potential energy changes in the process are negligible. $\mathrm{He}$ and $\mathrm{N}_{2}$ behaves as ideal gases. Specific heat capacities are constant.
Use the following data:
Ratio of specific heat capacities for $\mathrm{He}$ and $\mathrm{N}_{2}$ are $1.67$ and $1.4$, respectively.
Specific heat capacities at constant pressure for $\mathrm{He}$ and $\mathrm{N}_{2}$ are $5.19 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$ and $1.04 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$, respectively.
