Answer
$56,900~J$ of heat are required.
Work Step by Step
We can find the number of moles of hydrogen:
$PV = nRT$
$n = \frac{PV}{RT}$
$n = \frac{(10.0)(1.013\times 10^5~Pa)(250\times 10^{-3}~m^3)}{(8.314~J/mol~K)(273.15~K)}$
$n = 111.5~mol$
We can find the required heat:
$Q = c~n~\Delta T$
$Q = (20.4~J/mol~K)(111.5~mol)(25.0~K)$
$Q = 56,900~J$
$56,900~J$ of heat are required.
