Question

how much heat in joules is needed to raise the temperatureof 1.0 L of water from 0°C to 100°C? (Hint: Recall the originaldefinition of the liter.)

Answer 1

Given data:

Volume of water:

$V=1\text{ L}$

Converting volume from liter to cubic meter:

$\begin{gathered} V=1\text{ L} \\ =0.001m^3 \end{gathered}$

Density of water is ρ=1000 kg/m3. Therefore mass of 1 L of water is given as,

$\begin{gathered} m=V\rho \\ =0.001m^3\times1000kg/m^3 \\ =1\text{ kg} \end{gathered}$

The specific heat of water (heat required to rise the temperature by 1°C) is 4200 J/kg°C.

Therefore, the heat required to rise the temperature of water from 0°C to 100°C is given as,

$Q=mC(T_f-T_i)$

Here, m is the mass of water, C is the specific heat capacity of water, T_f is the final temperature and T_i is the initial temperature.

Substituting all known values,

$\begin{gathered} Q=(1\text{ kg})\times(4200\text{ J/kg}\cdot^{\circ}C)\times(100^{\circ}C-0^{\circ}C) \\ =420000\text{ J } \end{gathered}$

Therefore, 420000 J of heat energy is required to rise the temperature of 1.0 L of water from 0°C to 100°C.