Problem No: $5$ A rigid container contains $1$ mole of $H_2$ at $300K$ and $1$ bar. If $H_2$ can be

considered as an ideal gas, what is the total amount of heat required to increase its pressure from

$1$ bar to $2\mathrm{.}5$ bar $($You need to consider the temperature dependence of the molar heat capacity of

$H_2$; i$.$e$.,\{$:$Cp=a+bT+c{T}^2+d{T}^3)?$ If the autoignition temperature of $H_2$ is $500C,$ are we still safe

when we reach $2\mathrm{.}5$ bar? Which value would you calculate for the total amount of heat to increase

the pressure to $2\mathrm{.}5$ bar if you have used a constant heat capacity for $H_2?$