‘Tis the season to be heating

por Ulf Nobbmann, Friday, 23rd December 2022

On the northern hemisphere (where many of our offices are) we now have shorter days and lower temperatures, most prevalent of course in the higher latitudes. While this is not all gloom and doom it makes you appreciate a hot beverage so much more (think ‘Hygge‘). With an electric kettle we can get boiling water in no time. Yet, actually, how long does heating it take, and what’s involved in figuring this out?

Heating water kettle illustrating the electric heating of water, and how we can calculate from the power and mass how long it should take to boil a cup of tea, illuminated in festive green LED light.

Heating water

You may remember the old unit Calorie to measure caloric content? It was defined as the amount of energy needed to heat 1 g of water by 1 degree. In SI units this is about 4 Joule, so with 4 Joule we can increase the temperature of 1 g of water by 1 degree. Back to the kitchen, if we want to heat 1 Liter of water with an electric kettle of 2kW from 10°C to 60°C – how many Joules do we need?

…for a cup of tea…

We need to increase the water temperature by 50 degrees, this requires an energy of 4*50 J = 200 J per gram of water. For 1 Liter = 1 kg of water we then need 200 kJ of “heating” energy. So if the label on the electric kettle device states a power rating of 2 kW = 2 kJ/sec we should be able to supply the required energy in 100 seconds.

OK, you say, this might be a good example of why a little science and math can be helpful in everyday life. But what has that got to do with the instruments you normally write about?

…or in a Zetasizer?

When we perform a zeta potential light scattering measurement we apply an electric field to the sample, there is a voltage applied and an electric current travels through the liquid. The product of both (voltage times current) is the power, which we apply for a certain time – so are we then heating the sample during the measurement? This may be of interest, because in the interpretation of the data you may have to know the temperature or some parameter dependent on temperature, like viscosity. Will this heating increase the temperature in the cuvette and if so by how much?

Let’s take a specific example for the transfer standard: with an applied voltage of 150V, the measured current is about 1mA, in monomodal analysis the field is applied for about 1 sec, and that short subrun repeats about 10 times. We therefore have an applied power of about 150mW, and as a result of applying that for 10 sec we get 150 mW * 10 s = 1500 mJ = 1.5 Joule as the total applied energy. The amount of sample is about 800 µL, approximate that to 1000µL = 1 mL = 1 g of water. That means the sample heats less than half a degree (=1.5/4). In real life, the temperature change is probably even lower, since the sample holder chamber is temperature controlled, effectively reducing the heating effect by actively cooling against it (with the built-in Peltier). There are, of course, additional influences on the heating efficiency, thermal conductivity, thermal mass, geometry, etc that we ignored here. This is all just a ‘back-of-the-envelope’ calculation for this blog.

STEM – science, technology, engineering and mathematics

Malvern Panalytical as part of the Spectris Scientific Division is providing

leading scientific instruments and services, measuring particles down to the nano scale, helping customers better understand and shape everything from proteins, metals and polymers to controlling aseptic manufacturing.

Spectris Scientific Division, corporate website description

Thus our instrumentation relies on a skilled, knowledgeable workforce to invent, develop, build, and use our systems. This is so significant that a separate charity, the Spectris Foundation, specifically aims to improve access to a quality STEM education. Many partners around the globe are identified and supported through employee engagement, often combining donations with employee volunteering. Past examples we have featured on this site were Crack the Code mathematics or Celebrating Women in Science.

Maybe the above gave you some food for thought on why seemingly simple concepts like heating of water for a cup of tea can be relevant even in the design of sensitive scientific measurement equipment. Have a good holiday season!

Further reading