# Tea

Tea is a beverage prepared through the action of boiling water on tea leaves in a teapot. It is not a beverage prepared through the action of hot water on tea dust in a permeable bag dunked in a mug.

The choice of teapot has been controversial. The English tend to favour silver, well-polished by their butlers. There is a faction which favours china, and believes that china teapots are for use, not simply for display as ornaments.

The Great Teapot Debate

Those who despise silver teapots claim that it is the purpose of a teapot to keep hot tea hot, and silver, being an excellent conductore of heat, is about the worst possible material for the job.

Teapots lose heat through convection and radiation. Radiative losses are easy to calculate, being
σeA(T4-T04)
where σ, the Stefan Boltzmann constant, is 5.67×10-8 Wm-2K-4, e is the emissivity of the surface, A its area, and T the absolute temperature. The value of e for polished silver is less than 0.05, whereas for glazed porcelain it is about 0.9.

Equations for convective losses are harder, so I will simply assert that, for a surface of emissivity 0.9 at 90°C in a room at 20°C, the convective and radiative losses are approximately equal, at about 500W per square metre. Porcelain has a thermal conductivity of 1.5W/(mK) (compared to about 430W/(mK) for silver), so assuming a thickness of 0.5cm, porcelain's conductivity is 300W per square metre per Kelvin, and, for our purposes, silver's is large enought to be considered infinite.

Without doing any precise algebra, these figures suggest that, for teapots containing tea at 90°C a polished silver one will have its outside at 90°C and will be losing heat at about 500Wm-2, whereas a china one will have its outside at about 87°C and will be losing heat at about 1,000Wm-2.

We can perform a crude experiment by pouring a little over a pint of boiling water into the two (unwarmed) teapots, and recording the water temperature to the nearest 0.5°C at five minute intervals. The initial fall in temperature is governed by the heat capacities and thermal conductivities of the teapots, but, by chance, at the first five minute interval both recorded the same temperature.

 silver china 5 min 84.0°C 84.0°C 10 min 80.0°C 78.5°C 15 min 77.0°C 75.5°C 20 min 74.5°C 72.5°C 25 min 72.5°C 69.5°C 30 min 70.5°C 67.0°C

Though the results are closer than the above argument suggests, it is clear that the metal teapot is retaining heat better. The test is slightly unfair, as the teapots are different shapes. However, those who would expect the metal teapot to be significantly worse are confounded by these data.

It is also clearly important to warm the teapot. A pint of water has a heat capacity of about 2,400J/K, a 600g china teapot about 600J/K, and a 400g stainless steel teapot about 200J/K. So a pint of boiling water and a teapot at 20°C would be expected to equilibriate at 94°C for the metal teapot and 84°C for the china one before considering energy loss to the surroundings. In practice the temperature drop is slightly less as parts of the teapot, such as the handle, are quite well thermally isolated, and, in the above case, slightly more than a pint of water was used.