(Solved): 4.21 A rigid cylinder contains helium (molecular weight, 4) at a pressure of 5bar and a temperature ...

4.21 A rigid cylinder contains helium (molecular weight, 4) at a pressure of $$5\mathrm{bar}$$ and a temperature of $$15^{?}\mathrm{C}$$. The cylinder is now connected to a large source of helium at 10 bar and $$15^{?}\mathrm{C}$$, and the valve connecting the cylinder is closed when the cylinder pressure has risen to 8 bar. Calculate the final temperature of the helium in the cylinder assuming that the heat transfer during the process is negligibly small. Take $$c_v$$ for helium as $$3.17\mathrm{kJ}/\mathrm{kg}\mathrm{K}$$. $$\left(65^{?}\mathrm{C}\right)$$