Question

A water heater warms 35 l of water from a temperature of 22.7 c to a temperature of 83.7

Answer 1

The amount of energy needed to increase the temperature of a substance by $\Delta T$ is given by
$Q=m C_s \Delta T$
where
m is the mass of the substance
$C_s$ is its specific heat capacity
$\Delta T$ is the increase in temperature

The water volume is $V=35 L= 35 dm^3 = 0.035 m^3$, since its density is $d=1000 kg/m^3$, the mass of this sample of water is
$m=dV=(1000 kg/m^3)(0.035 m^3)=35 kg$

The water specific heat capacity is $C_s = 4.18 kJ/kg ^{\circ}C$

and the increase in temperature is $\Delta T=83.7 ^{\circ}C-22.7 ^{\circ}C=61^{\circ}C$

Therefore, the amount of energy needed is
$Q=mC_s \Delta T=(35 kg)(4.18 kJ/kg ^{\circ}C)(61^{\circ}C)=8924 kJ = 8.92 \cdot 10^6 J$