The amount of heat 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 its specific heat capacity
[tex]\Delta T[/tex] is the increase of temperature
The sample of silver of our problem has a mass of [tex]m=24.7 kg[/tex]. Its specific heat capacity is [tex]C_s = 236 J/g^{\circ}C[/tex] and the increase in temperature is
[tex]\Delta T=30.0^{\circ}-14.0^{\circ}C=16.0^{\circ}C[/tex]
Therefore, the amount of heat needed is
[tex]Q=mC_s \Delta T=(24.7 kg)(236 J/g^{\circ}C)(16.0^{\circ}C)=9.32 \cdot 10^4 J[/tex]
