The temperature of $3\mathrm{.}37$mol of an ideal diatomic gas is increased by $56\mathrm{.}9C$ without the pressure of the gas changing. The molecules in the gas rotate but do not oscillate. $($a$)$ How much energy is transferred to the gas as heat? $($b$)$ What is the change in the internal energy of the gas? $($c$)$ How much work is done by the gas? $($d$)$ By how much does the rotational kinetic energy of the gas increase?