The amount of energy needed to increase the temperature of a substance by [tex]\Delta T[/tex] is given by:
[tex]Q=m C_s \Delta T[/tex]
where
m is the mass of the substance
[tex]C_s[/tex] is the specific heat capacity of the substance
[tex]\Delta T[/tex] is the increase of temperature
In our problem, [tex]m=755 g[/tex], while
[tex]\Delta T=403 K-283 K=120 K[/tex]
and the specific heat capacity of iron is
[tex]C_s =0.45 J/gK[/tex]
if we plug these numbers in the equation, we find the amount of energy needed:
[tex]Q=mC_s \Delta T=(755 g)(0.45 J/gK)(120 K)=4.08 \cdot 10^4 J[/tex]
