Heating Water with an Electric Stove

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Source: High school physics (Chinese)

Problem

An electric stove with power $2$ kW is used to heat $2$ kg of water from $20\,^\circ\text{C}$ to $100\,^\circ\text{C}$. The efficiency of the stove is $30\%$. The specific heat of water is $4.2 \times 10^{3}$ J/(kg$\cdot{}^\circ$C).

How much time is required?
$t = 1120$ s $\approx 18.7$ min

The useful heat absorbed by the water is:

$$Q = m c \Delta T$$

The energy delivered by the stove is $P t$, of which only the fraction $\eta$ is useful:

$$\eta P t = m c \Delta T$$

Solving for $t$:

$$t = \frac{m c \Delta T}{\eta P}$$

Substituting $m = 2$ kg, $c = 4.2 \times 10^{3}$ J/(kg$\cdot{}^\circ$C), $\Delta T = 80\,^\circ\text{C}$, $\eta = 0.30$, $P = 2000$ W:

$$t = \frac{2 \times 4.2 \times 10^{3} \times 80}{0.30 \times 2000} = \frac{6.72 \times 10^{5}}{600} = 1120 \text{ s} \approx 18.7 \text{ min}$$