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