Heat capacity $C$ is not well-defined for a closed system undergoing constant temperature processes, at least with a reversible process. For a reversible process in a closed system,
$$\delta q_\pu{rev} = C\pu{d}T.$$
If temperature is constant, then $\mathrm{d}T=0$ gives $q_\pu{rev} = 0$ for any finite value of $C$. Other formulae for heat capacity, expressed through internal energy or enthalpy, require additional constraints such as constant volume or pressure, and only expansion work is allowed. Neither of these alternative depictions change the outcome.
This is not a problem because heat capacity does not make sense anyway if we assume a priori that temperature cannot change at all.
My attempt: Since $\ce{H2}$ is a diatomic gas, its $C_P$ is $7R/2$ which gives $\pu{7 cal mol-1 K^-1}$.
I would be fine with this answer as well. If heat is supplied at constant pressure to a closed non-reactive system, then the temperature must change. The alternative would be an change in volume to keep temperature constant but this would alter the pressure of the system.
In other words, in the net-constant pressure and net-constant temperature process dihydrogen had to warm up (according to its heat capacity at constant pressure), and then cool off again. It is not a good idea to equate the heat capacity here to infinity; that would make little physical and mathematical sense in my opinion.