Question $4(12$ marks$)$

Sample A $(5$kg$)$ initially at $(100,$ and sample B $(3kg)$ initially at $20C$ are placed in a thermally insulated container and allowed to come to thermal equilibrium of $40C$ Given the specific heat of sample A is $500Jk{g}^{-1}{K}^{-1}.$

$($a$)$ Determine the specific heat of sample B$.$

$(6$ marks$)$

$($a$)$ Find the entropy change of the whole system.

$(6$ marks$)$