Pasta Quick! – thinking through the science (part 2)”

The second part of the experiment gets us thinking more about the cost and the carbon cost.

Many people boil water in an electric kettle before pouring into the pan to cook pasta. So is this a really good idea for cost and what does it mean for greenhouse gas emissions?

Suitable for Key Stage 4 (ages 14-16).

Skills: Being confident with Units, using Formulae, introducing Costing, Comparisons and Chemistry.

Here we look at two extra tasks related to the first part of the experiment. The first section looks at costs and the second section looks at the wider environmental effects of one our choices by examining the equivalent carbon dioxide emissions for the two options in the practical experiment in part 1.

Cheaper Pasta

Consider which one costs more.

From your energy bills you will have a unit rate in pence per kWh for both gas and electricity.

If you don’t have access to your bill then you can use these values that were typical of UK bills in 2019.

Cost of gas use = 3.8 pence per kWh

Cost of electricity use = 14.4 pence per kWh

Notice that the gas units saving when using an electric kettle is the energy used to boil water on the gas compared to the energy used to boil water in a kettle. Now we can see the advantages and disadvantages of boiling water on the gas hob compared to the gas kettle.

In the example here, the kettle rating plate says 1850 W to 2200 W. The kettle took 4 min 11 sec (251 s) to boil water. That is between 0.129 kWh and 0.153 kWh. We could approximate that as 0.14 kWh. Using only gas to heat and boil water and pasta, 0.0274 units were consumed (for the pan with a lid). When we speeded up the initial water boiling using the electric kettle, only 0.0083 units were consumed for the pan with a lid. The gas units saved by using the electric kettle were 0.0274 – 0.0083 = 0.0191 units. Converting to kWh using the formula gives 0.0191 x 1.02264 x 39.4 / 3.6 = 0.214 kWh. So even if we used the high power estimate for the electric kettle, boiling water using an electric kettle uses less energy (at point of heating).

Why is that? The young scientist might want to think about why that might be. What is being heated? How much heat is being lost to the surroundings? How much is going to where it is required (the water)? To get to close to 100% efficiency we would need to heat only the water and keep everything else including the kettle or pan cool.

What about costs?

In this example,

Electric kettle heating cost = 1.86p to 2.20p (approximately 0.14 kWh x 14.4 p/kWh = 2.02p)

Gas heating cost = 0.214 kWh x 3.8 p/kWh = 0.81p

So advantages and disadvantages of using a kettle to boil the water first may be something like:

AdvantagesDisadvantages
Time – halves the overall cooking timeCost – about 40% cost to use gas for first boil
Energy – 65% energy used for first boil

Friendlier Pasta

Consider which one emits more carbon dioxide.

We know that carbon dioxide emissions coming from fossil fuels are the major contributor to global warming and climate change. Here we calculate the carbon dioxide emissions for the experiment.

Gas

When we burn with natural gas we combust methane with the oxygen in the air to generate heat. As a result we produce carbon dioxide and water vapour. Methane is the lightest hydrocarbon gas and is made up of one carbon atom and four hydrogen atoms and is written symbolically as CH4. The oxygen molecule makes up about 21% of the volume of the air around us and has the chemical symbol O2. The combustion equation can be written:

CH4 + O2 → CO2 + H2O

This needs to be balanced. We need to have as many Cs and Os and Hs on the left as the right. Can you add some multiples of O2, CO2 and H2O to make it work?

[Ans: CH4 + 2O2 → CO2 + 2H2O]

So combustion of one molecule of methane generates one molecule of carbon dioxide.

How do we calculate the carbon dioxide emissions of the units of gas we use?

Remember that one unit of gas is one cubic metre of gas. One metre is 100cm or 10dm. So one cubic metre is 100cm x 100cm x 100cm or 10dm x 10dm x 10dm = 1 000 000 cm^3 or 1000 dm^3.

You may know that the molar volume of any gas at room temperature and pressure is 24 dm^3.

Ideal gas law

What we want is the molar volume of gas at 15°C and 101325 Pa, because those are the conditions for the corrected units (units x 1.02264). To be accurate we will have to use the ideal gas law

Vm = V/n = RT/P

where R is the universal gas constant and is 8.314 463 m^3 Pa K^-1 mol^-1, T is the temperature in Kelvin (K) and P is the pressure in Pascals (Pa). Vm is the molar volume in m^3 (V is the actual volume and n is the actual number of moles).

Vm = 8.314 463 m^3 Pa K^-1 mol^-1* (273.15+15) K / 101325 Pa = 0.023 644 8 m^3/mol or 23.645 dm^3/mol (quite close to the room temperature value of 24 dm^3/mol we often use).

So how many moles of gas did we burn?

[Hint: multiply the units by 1000/24, because we want to convert m^3 to dm^3 (x 1000) then divide by the molar volume of a gas at room temperature and pressure (24 dm^3)]

Now we know how many moles of methane we burnt, we also know how many moles of carbon dioxide we released. We now need to convert to mass of carbon dioxide (g or kg if you prefer).

Do we know the molar mass of the elements? In g/mol?

Can we calculate the molar mass of carbon dioxide?

[Hint: C = 12 g/mol, H = 1 g/mol, O = 16 g/mol]

[Ans: CO2 = 44 g/mol]

So now we can calculate the grams of carbon dioxide released:

[Hint: number of moles multiplied by the molar mass]

Direct Emissions

If we had burnt 1 unit of gas (1 m^3), we would have released 1000×1.02264/23.645*44 = 1903 g or 1.90 kg according to our calculation.

The official UK figure for “direct” emissions is actually 2.02 kg per m^3 (for carbon dioxide equivalent). Why is this more?

* One reason is that natural gas supplied is only around 92% methane, with around 3% being ethane (C2H6), 0.5% propane (C3H8) and smaller amounts of bigger hydrocarbons. As we burn the bigger hydrocarbons we have larger ratios of carbon to hydrogen and more carbon dioxide released on combustion per mole of hydrocarbon:

C2H6 + 3.5O2 → 2CO2 + 3H2O

C3H8 + 5O2 → 3CO2 + 4H2O

* A secondary reason is that during combustion we also release small quantities of nitrous oxide (N2O) and unburned methane (CH4). These gases are actually much more powerful greenhouse gases than carbon dioxide with a 100-year equivalence to carbon dioxide as 298 times more powerful and 25 times more powerful than carbon dioxide respectively. So we only need small quantities of them to start pushing the figure towards the 2kg/m^3 figure for carbon dioxide equivalent emissions.

Indirect Emissions, or Well-To-Tank (WTT) Emissions

It actually turns out that the emissions at point of combustion (direct), in other words those released in your kitchen, are not the entire story. We really have to take into account the energy used to get the gas out of the ground and into your kitchen and losses along the way (such as methane leakage along pipelines). This part is called Well-to-Tank often abbreviated to WTT emissions.

The official UK figure for WTT emissions is 0.26 kg per m^3 (for carbon dioxide equivalent).

So calculating the equivalent grams of carbon dioxide produced as a result of combustion and supply mean we need to account for 2.28 kg per m^3. For our units that would be Units x 1.02264 x 2280 g/m^3. The UK government also publishes figures for g per kWh (207.8 g/kWh).

Have a go at calculating the overall emissions from the gas we used in our experiment here:

Electricity

What about the electrical energy used to power the kettle. Clearly we don’t have any carbon dioxide release in the kitchen, but we had to generate that electricity.

Average UK grid electricity in 2019 split by generation type was:

Type% of total generationCarbon intensity gCO2eq/kWh
Coal2.18820
Oil0.35650
Gas41.67490
Biomass11.78230
Nuclear17.7412
Solar4.0845
Hydroelectricity1.8724
Wind (onshore)10.1711
Wind (offshore)10.1512
Re-adjusted 2019 UK generation mix and typical world average IPCC carbon intensities

Where does this data come from? The total generation mix for the UK grid is collected as official statistics for the government. Here the % has been re-adjusted very slightly because there are small amounts which are pumped storage, other fuels and shoreline renewables. We’ve made the assumption that they don’t change the overall carbon intensity of the grid.

The carbon intensity numbers come from the Intergovernmental Panel on Climate Change (IPCC) assessment report from 2014. They reflect the typical carbon intensities of the various generation types. The reason renewables and nuclear are not zero is because these figures include the carbon dioxide released during building and manufacture.

Let’s calculate the average UK grid carbon intensity for 2019

The average carbon intensity is 0.0218 x 820 + 0.0035 x 650 + … = 258 g/kWh

Can you complete the calculation and check the answer?

And just like gas, there is also a carbon cost for distribution and supply. For the UK this is 20 g/kWh.

So the carbon intensity of standard grid electricity is 278 g/kWh.

You could have a go at checking the carbon intensity of your electricity supply. Note that even renewable supplies will have a carbon intensity above zero.

Returning to the example,

Electric kettle heating carbon cost = 35.9g to 42.5g (approximately 0.14 kWh x 278 g/kWh = 38.9g)

Gas heating carbon cost = 0.0191 units x 1.02264 x 2280 g/m^3 = 44.5 g

(We can check that using the kWh approach = 0.214 kWh x 207.8 g/kWh = 44.5 g)

Updating the advantages and disadvantages table (for using a kettle to boil the water first) becomes:

AdvantagesDisadvantages
Time – halves the overall cooking timeCost – about 40% cost to use gas for first boil
Energy – 65% energy used for first boil
Carbon – 90% of carbon compared to gas

Are you surprised at the very little difference between carbon dioxide equivalent emissions for using an electric kettle and using the gas stove to boil water? It’s very easy to see that with just a bit more carbon intensity (like the UK was right up to 2017) the gas option was better.

The gas option might still be better depending on the energy mix on the grid right now. Have a look:

https://www.electricitymap.org/map

What is the carbon intensity of the UK grid right now?

How does the UK grid compare with other countries? Write down some low carbon grids and have a look for high carbon grids.

Of course an easy way for us to reduce the carbon intensity is to purchase nuclear power or renewables. The carbon cost is still not zero, but it is much much better. If we bought only Wind or Nuclear power we would expect the carbon intensity (including supply) to be around 32 g/kWh. With our example that would mean 0.14 kWh x 32 g/kWh = 4.5 g. At 10% of gas, the equivalent carbon dioxide emissions are now really low.

What have you learnt? Note down the best things we could do to reduce carbon dioxide emissions when boiling water? Tell your parents about them.