In a chemical plant, hydrogen gas with a flow rate of $0\mathrm{.}1$ is cooled from $500$ K to $13$ K with nitrogen gas in a countercurrent heat exchanger. Nitrogen gas enters the heat exchanger at $300$K and exits at $323$K$.$ During this process, heat is released to the environment at a rate of $36$kJ$/$s$.$ Assuming that the gas behaves ideally and its temperature to the environment is $300$K$,$ calculate the entropy formation rate for this process.