A piston-cylinder arrangement contains an ideal gas mixture of $4 \: \mathrm{kg}$ of hydrogen and $13 \: \mathrm{kg}$ of nitrogen at $250 \: \mathrm{K}$ and atmospheric pressure. On heat addition, the mixture expands at constant pressure until the temperature rises to $350 \: \mathrm{K}$. The average isobaric specific heats $\left(c_{p}\right)$ for hydrogen and nitrogen are $14.239 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$ and $1.040 \mathrm{~kJ} / \mathrm{kg}-\mathrm{K}$, respectively. The amount of heat (in $\mathrm{MJ}$) added to the cylinder is $\_\_\_\_\_\_\_$ (rounded off to three decimal places).
