Question

if a metal object was cut on half how much heat will be required to raise both half to a specific temperature

Answer 1

suppose the mass of a metal object be m and its specific heat capacity be s, and, H joules of heat is required to raise its temperature by t degrees Celsius

Than H is given by relation, $H = mst$

Now if this object is cut in two half's, than mass of half part will also be half i.e. M/2

So heat required to heat the half part will be $= (\frac{m}{2}) st =\frac{mst}{2} = H/2$  

Hence, the heat required to raise the half object to a specific temperature will also become half.