MET Question. Some help needed

[XL319]

I was looking at this question and although I got the question right albeit a bit of a guess. I am struggling to work the temperature error out. The difference between ISA and actual temp is 13.5, but when I tried to work it out it came out at 21500 or something. Obviously it is colder so you will be lower than FL300

Q. You are flying at FL 300 where the outside air temperature is -57.5°C and the pressure at MSL is 1013.25 hPa. If you assume that the difference between the actual temperature and the temperature in the ISA is valid for the whole troposphere, then the true altitude is:
A. 27000
B. 30000
C. 28500
D. 31500

C is the right answer. Anyone shed any light on this thanks.

[Alex Whittingham]

The ISA temperature at FL300 is (30 x -2°) + 15° = -45°
The temperature deviation is therefore (-57.5°) - (-45°) = -12.5°
The temperature correction is 4% for every 10° deviation from ISA which is:
(-12.5°/10) x 30,000ft x 0.04 = -1500ft
The true altitude is therefore 30,000ft - 1,500ft = 28,500ft

[12Watt Tim]

2 degrees per thousand feet Alex? Not using JSA are we?

[Alex Whittingham]

Guilty! For the purists:

The ISA temperature at FL300 is (30 x -1.98°) + 15° = -44.4°
The temperature deviation is therefore (-57.5°) - (-44.4°) = -13.1°
The temperature correction is 4% for every 10° deviation from ISA which is:
(-13.1°/10) x 30,000ft x 0.04 = -1572ft
The true altitude is therefore 30,000ft - 1,572ft = 28,428ft,

closest answer (C)

I would always use 2° per thousand feet. Its only an approximate calculation anyway.

[12Watt Tim]

I know - I only put it because I had just worked it with ISA out and you had beaten me to posting!

[XL319]

Of course. So simple it was staring me in the face. Thanks very much guys.

P.S. I'll stick to 2degrees Alex... insteasd of 1.98