If climbing at a constant Mach number up to the tropopause under ISA conditions, what happens to TAS?

When climbing at a constant Mach number under ISA (International Standard Atmosphere) conditions, the true airspeed (TAS) will actually decrease as you ascend towards the tropopause. This is due to the relationship between Mach number, true airspeed, and temperature.

Mach number is defined as the ratio of the true airspeed (TAS) to the speed of sound (A). As altitude increases, the air temperature generally decreases until reaching the tropopause. This decrease in temperature results in a corresponding decrease in the speed of sound. Since the Mach number is held constant during the climb, and the speed of sound decreases with altitude, TAS must also decrease in order to maintain that constant Mach number.

Therefore, while climbing at a constant Mach number, the TAS will decrease as the environmental conditions change, specifically the drop in temperature which reduces the speed of sound.