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*1000kg/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})*(4200\text{ J/kg}\cdot^(\circ)C)*(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.