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I look after a which I hope will achieve an accuracy of less than 1 second of error per year. It has a temperature-compensated pendulum, but is sensitive to air pressure variation. If the mean global temperature was to rise by, say, 4 掳C, would there be any change to mean air pressure at sea level? Put simply, would global warming cause the clock to speed up or slow down?
鈥� The accuracy of a pendulum clock is affected by changes in the density of the air surrounding the pendulum. That鈥檚 because the air exerts a slight buoyant force on the bob, counteracting the downward pull of gravity, while friction between the bob and the air effectively increases its mass. Both effects slow down the clock, the degree of slowing being dependent on the density of the bob and also its shape. A typical pendulum clock might lose around 40 seconds per year for a 1 per cent increase in air density.
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The density of air depends on its temperature and pressure, and on the average molecular weight of the gases that make it up. A reduction in temperature from 20 掳C to 19 掳C will increase air density by about 0.34 per cent and so slow the clock by some 14 seconds per year. We do not need to concern ourselves with this, however, as it is taken into account in the way a clock pendulum is temperature-compensated to minimise the effect of thermal expansion.
鈥淎 reduction in air temperature from 20 掳C to 19 掳C slows a pendulum clock by 14 seconds a year鈥�
A pressure increase of 1 millibar (100 pascals) increases air density by 0.1 per cent and slows the clock by about 4 seconds per year. Some clocks have a barometric compensation device built into the pendulum and some are even put inside isobaric chambers to avoid the problem altogether.
The main source of variability in the average molecular weight of air is its water vapour content. At 16 掳C, a rise in relative humidity (RH) from 30 to 40 per cent would reduce air density by 0.07 per cent and speed up the clock by some 3 seconds per year.
If we keep RH constant, we would find the amount of water vapour that air can hold nearly doubles for every 10 掳C rise in temperature. If the whole atmosphere warmed by 4 掳C, its water-vapour content would increase by around 30 per cent, assuming no change in RH overall. This would increase the total mass of the atmosphere and the pressure at sea level would rise by about 0.7 millibars, which would slow the clock by about 3 seconds per year.
However, this would be offset by an increase in the RH of the clock鈥檚 local environment, which is likely to occur unless air-conditioning is used. The increase in RH at fixed temperature mentioned above would exactly cancel out the previous effect.
As is so often the case, the answer to the question is really 鈥渋t depends鈥�.
Chris Terry, Teddington, Middlesex, UK