Final answer:
The true airspeed at FL 240 with a temperature of -25 degree C, a calibrated airspeed of 348 knots, and a true mach of .81 is approximately 715.74 knots.
Step-by-step explanation:
To calculate the true airspeed, we need to convert the calibrated airspeed to equivalent airspeed (EAS) first. EAS is the airspeed corrected for altitude and temperature. We can use the equation: EAS = CAS * SQRT((T0+L * H) / (T + L * H)), where CAS is the calibrated airspeed, T0 is the standard temperature at sea level, L is the temperature lapse rate, and H is the altitude in feet. Once we have the EAS, we can calculate the true airspeed (TAS) using the equation: TAS = EAS * SQRT(d0 / d), where d0 is the standard air density at sea level and d is the air density at the given altitude and temperature.
In this case, the altitude is given as FL 240, which is equivalent to 24000 feet. The temperature is given as -25 degree C. Using the equations, we can calculate the EAS and then the TAS.
EAS = 348 * SQRT((288.15 - 0.0065 * 24000) / (273.15 - 0.0065 * 24000)) = 348 * SQRT(1.0865 / 0.8765) = 348 * 1.0946 = 380.85 knots
TAS = 380.85 * SQRT(1.225 / (0.393 * (-25 + 273.15 + 0.001 * 24000))) = 380.85 * SQRT(1.225 / 0.4383) = 380.85 * 1.8819 = 715.74 knots
Therefore, the true airspeed at FL 240 with a temperature of -25 degree C, a calibrated airspeed of 348 knots, and a true mach of .81 is approximately 715.74 knots.