How Expensive does a Kettle Boil Water?

In an earlier post, I have analyzed and tested the time required by an electrical kettle to boil water. Let's focus on a more practical money issue here: how much do you need to pay for boiling water?

Theoretical Derivation of the Estimation Formula

First of all, we need to know that many electricity providers worldwide use the unit kWh (kilowatt-hour) to calculate the energy usage and charges. It is defined to be the multiplication of kilowatt (1,000W) and hour. Therefore, it would be convenient if we can derive a formula that expresses the energy in kWh.

To calculate the energy required to boil water, we don't need to reinvent the wheel but to use the result obtained from an earlier post. In particular, the time required to boil water is

$!t \approx \frac{4200 \times V \times (100-T_i)}{P} \; \mathrm{seconds}$

where we use units second, watt, litre, and celsius for the time required $t$, the power rating $p$, the volume of the water $V$, and the initial temperature $T_i$ respectively.

Rewrite the formula to calculate the energy $W$ consumed:

$!W = Pt \approx 4200 \times V \times (100-T_i)$.

To express the energy with the unit kWh, we can change $P$ and $t$ to use kilowatt and hour respectively. In this case, we have

$!W = \frac{1}{1000}P \cdot \frac{1}{60\cdot 60} t \approx \frac{1}{3600000} \cdot 4200 \times V \times (100-T_i) \; \mathrm{kWh}$.

By taking approximation and by substituting $V=1$, we obtain the energy required to boil one litre of water:

$!W \approx \frac{100-T_i}{850} \; \mathrm{kWh}$

Great! It looks simple enough for rough estimation.

Some Examples

Every country has its own billing system for electricity. Let's consider the case in Malaysia. According to the domestic rate imposed by Tenaga Nasional Berhad [www2.tnb.com.my] as of this writing (it has been rumored for quite some time to be raised soon), every kWh (of the first 200kWh per month) is charged for RM0.218. When $T_i=28$ (Celsius), which is common here, boiling one litre of water requires about

$!\frac{100-28}{850} \times \mathrm{RM}0.218 \approx \mathrm{RM}0.0184$.

Well, just about 2 Malaysia cents, not bad.

How about Singapore? According to the domestic rate imposed by Singapore Power [www.singaporepower.com.sg] as of this writing (valid from 1st July until 31 March 2006), every kWh is charged for S\$0.2115. When $T_i=28$ (Celsius), which is common in Singapore, boiling one litre of water requires about

$!\frac{100-28}{850} \times \mathrm{S\$}0.2115 \approx \mathrm{S\$}0.0179$.

Well, about 2 Singapore cents, not bad too.

Doctors advise us to drink at least 2 litre of water everyday. So, if you drink boiled water, you spend about RM0.04 or S$0.04 everyday.

You can perform similar calculation for other electrical appliances. The concept and the calculation are not difficult if you studied high-school physics before.