Use the worked example above to help you solve this problem. A cylinder contains $2\mathrm{.}10$ mol of helium gas at $20\mathrm{.}0$C$.$ Assume that the helium behaves like an ideal gas.

$($a$)$ Find the total internal energy of the system.

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$($b$)$ What is the average kinetic energy per molecule?

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$($c$)$ How much energy would have to be added to the system to double the rms speed? The molar mass of helium is $4\mathrm{.}0010-3$ kg$/$mol$.$