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 its specific heat capacity
[tex]\Delta T[/tex] is the increase in temperature
The water volume is [tex]V=35 L= 35 dm^3 = 0.035 m^3[/tex], since its density is [tex]d=1000 kg/m^3[/tex], the mass of this sample of water is
[tex]m=dV=(1000 kg/m^3)(0.035 m^3)=35 kg[/tex]
The water specific heat capacity is [tex]C_s = 4.18 kJ/kg ^{\circ}C[/tex]
and the increase in temperature is [tex]\Delta T=83.7 ^{\circ}C-22.7 ^{\circ}C=61^{\circ}C[/tex]
Therefore, the amount of energy needed is
[tex]Q=mC_s \Delta T=(35 kg)(4.18 kJ/kg ^{\circ}C)(61^{\circ}C)=8924 kJ = 8.92 \cdot 10^6 J[/tex]
