Question

Calculate the heat that must be supplied to

Answer 1

Q must be supplied = 119523.3~J

Further explanation  

The law of conservation of energy can be applied to heat changes, i.e. the heat received/absorbed is the same as the heat released  

Q in = Q out  

Heat can be calculated using the formula:  

Q = mc∆T  

Q = heat, J  

m = mass, g  

c = specific heat, joules / g ° C  

∆T = temperature difference, ° C / K  

So from the question :

Q to the system(Q supplied) = Q water + Q steel vessel(Q gained)

$\tt Q~supplied=m.c\Delta T(water)+m.c\Delta T(vessel)\\\\Q~supplied=375\times 4.18\times (100-35)+532\times 0.51(100-35)\\\\Q~supplied=101887.5+17635.8=119523.3~J$