Question

Suppose that you had water in a pot on a stovetop. Neglecting the material that the pot is made out of, and neglecting heat energy lost use to other processes, how long would it take for a 1000 W stovetop to raise 2.68 kg of water from 18.2oC to 53.2oC? The specific heat of water in this state is 4186 J/kg-oC. HINT: Find the amount of heat first, then look at the equation for power.

Answer 1

We are given the following information

Mass of water: m = 2.68 kg

Initial temperature: T1 = 18.2 °C

Final temperature: T2 = 53.2 °C

Power: P = 1000 W

Specific heat capacity of water: c = 4186 J/kg °C

We are asked to find the time required to change the temperature of the water.

Recall that the amount of heat required is given by

$\begin{gathered} Q=m\cdot c\cdot\Delta T \\ Q=m\cdot c\cdot(T_2-T_1) \\ Q=2.68\cdot4186\cdot(53.2-18.2) \\ Q=392646.8\; J \end{gathered}$

So, the amount of heat is 392646.8 joules.

Recall that power is given by

$P=\frac{Q}{t}$

Let us solve for time (t)

$\begin{gathered} t=\frac{Q}{P} \\ t=\frac{392646.8}{1000} \\ t=392.6468\; s \end{gathered}$

Therefore, the required time is 392.6468 seconds.

(Please round off as per instructions)