$($a$)$ Determine the temperature rise in a mass concrete member after $7$ days. The mix proportion of concrete is $1$:$1\mathrm{.}60$:$2\mathrm{.}40$:$0\mathrm{.}50($Cement : Fine aggregate: Coarse aggregate : Water$).$ Assume that the Heat of hydration of cement after $7$ days $=500k\frac{J}{k}g$; Specific heat of water $=4\mathrm{.}18k\frac{J}{k}\frac{g}{}C$; Specific heats of solids $=0\mathrm{.}22$ times that of water. $($Answer: $74\mathrm{.}7C)$

$($b$)$ If the $30\%$ heat loss is expected near the surface due to lower ambient temperature, what will be the concrete temperature near the surface? $($Answer: $($:$52\mathrm{.}3C\}$

$($c$)$ If you have decided to replace $20\%$ of cement with fly ash, what will be the rise in temperature after $7$ days at the core and near the surface? Assume negligible heat evolved by the pozzolanic reaction of fly ash. $($Answer: $59\mathrm{.}8C,41\mathrm{.}8C)$