Then: $($a$)$ Taking as given that the specific internal energy of an ideal gas is independent of the gas pressure, justify the claim that $$& for a process in which an ideal gas goes from $($T$1,$ P$1)$ to $($T$2,$ P$2)$ equals $$& for the same gas going from T$1$ to T$2$ at a constant pressure of P$1.$

$($b$)$ Calculate $$& $($cal$)$ for a process in which the temperature of $2\mathrm{.}5$ mol of an ideal gas is raised by $50\backslash$deg C$,$ resulting in a specific internal energy change $$& $=3500$ cal$/$mol