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Aircraft use barometric altitude, e.g. FL300 is the barometric altitude of 30,000 ft MSL. In winter however, FL300 is actually lower than the absolute altitude of 30,000 ft because of a cold and therefore compressed atmosphere, and in summer FL300 should be higher than 30,000 ft because the heated up atmosphere stretches itself out.

Does this mean that in summer it would be more difficult for a plane to reach a certain barometric altitude (e.g. FL300) than in winter? Is it more likely for planes to fly at higher barometric altitudes / flight levels in winter because they don't have to fly up a way as long as in summer?

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The published performance data is based on the International Standard Atmosphere, being 15°C and 1013 hPa at sea level and decreasing at a standard lapse rate with altitude until you're in the stratosphere where it's constant.

Stratospheric temperatures can be colder or warmer than the ISA temperature in the flight levels, and the time of year is a factor (also affecting the tropopause level - in the arctic in winter, the stratosphere may start in the teens).

So an airplane may have a service ceiling of FL410 at ISA but the actual flight level will be higher if temperatures are below ISA or lower if above ISA.

Performance charts will include charts for ISA deviations, for example ISA + 5, ISA + 10 etc. A hot summer day may be ISA + 15 in the stratosphere. The CRJ200, on an ISA +15 day could not get to its FL410 ceiling no matter how patient you were, letting it take its time, in mach mode. On the other hand on an ISA -10 day in winter, you might be able to coax it to FL420 it you're patient and careful, although flying right at ceiling is a dangerous place to be for the unwary.

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There are a few misconceptions in this question that we need to address before it can actually be answered.

While there is a very slight seasonal variation in the average sea-level atmospheric pressure (and that pressure is actually slightly lower in the winter), weather phenomena such as high and low pressure cells, fronts, etc. have a much greater effect on atmospheric pressure than the time of year.

Now, on to the actual question. The "ease" with which an airplane climbs is related to the air pressure, not the absolute altitude. All else being equal, going from, say, FL200 to FL300 always takes the exact same amount of effort, regardless of the actual distance to the ground. (If the air is less dense than average, the airplane will burn a tiny bit more fuel going the longer vertical distance to reach the same flight level, so I guess you could say that that requires a little more effort, depending on how you define "effort".)

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Does a plane's service ceiling vary with season/temperature?

An airplane's Service Ceiling is generally defined as the maximum altitude above mean sea level (MSL) that can be reached at the point it's maximum rate-of-climb (ROC) has decreased to 100 ft per minute (FPM). When it's published in an AFM or POH it's calculated based on standard atmospheric conditions (ISA), which rarely exist.

To simplify an answer to your question, with all other circumstances remaining the same (e.g. airplane weight), the higher the temperature the lower the functional service ceiling will be above MSL (true altitude).

So generally in the summer (when/where temperatures are warmer) the functional service ceiling will be reached at a lower true altitude above MSL. The opposite would be true in the winter when/where temperatures are colder. It's all about aircraft/engine performance capability based on an increase or decrease of the density altitude the aircraft is operating at.

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