The mean air pressure at sea level is most simply a function of the mass of the atmosphere. This in turn is a function of two components, the mass of each molecule in the atmosphere and the number of molecules of any given mass. By heating or cooling any particular volume of the atmosphere we cause transient local pressure changes as a result of expansion and convection, but no significant effect on mean air pressure. If global warming were to cause a marked increase in extremes of weather, that certainly might affect your clock, though obviously not in any consistent direction.

There is however another factor. Higher temperatures might be expected to increase the volatility of many substances on the planet, of which far and away the major example would be water. For example if a great deal of water were to evaporate from the mid-latitudes and precipitate as ice in the polar latitudes, this might start a positive feedback cycle reducing mean atmospheric humidity. In other words there would be less atmosphere and mean pressure would drop. Conversely, if increasing amounts of water were to remain in the atmosphere, mean atmospheric pressure would indeed increase.

Increasing the mass of molecules, eg by replacing oxygen with carbon dioxide would increase the pressure, but at a few hundred parts per million, the increase would require some very sensitive measurement to detect it!

I love the sound of your clock!

Jon

If atmospheric warming does not alter the mass of the atmosphere and provided gravity does not change then the sea-level pressure will be about 101325 Pascals, no matter what the atmospheric temperature is so that sea-level pendulum clocks will not experience any more air-friction than before. What will happen is that the atmosphere expands as it warms and this will cause a rise in air-pressure at a fixed height above sea-level – say, up a mountain. This happens because a larger fraction of the atmosphere will be above the fixed height, causing a greater pressure than before to be recorded. In fact, this idea has been used to show that the thermometer-based estimates of temperature changes through the 20th century are correct – a temperature-estimate based on records of mountain-station barometer readings, and sea-level pressures showed the same pattern as thermometer readings – warming to the 1940’s, cooling to about 1970 and warming since then.

However, rigorously and in reality, as a warmer atmosphere does hold more moisture the mass of the atmosphere will increase with warming and thus even sea-level pressures will rise a bit and friction on the pendulum clocks of the world will increase, slowing them down a bit.

Peter Thejll, Danish Climate Centre.

You say it's sensitive to air pressure, so I'd worry about the normal variations in barometric pressure.

The accuracy of a pendulum clock is affected by changes in the density of the air surrounding the pendulum. That's 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.

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 °C to 19 °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.

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 °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 °C rise in temperature. If the whole atmosphere warmed by 4 °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's 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 "it depends".

Chris Terry, Teddington, Middlesex, UK