Just looking in my MERM... I kind of agree that whether it's R or F in the formula, they should cancel.
In looking at the solutions, the equation in question looks like the one they use to feed into 29.99, which is 29.18.
In 29.18, since they use a multiplier T2 = T1(p2/p1)^((k-1)/k)) that the units need to be in R.
Once you have solved for T2 from that, then you can plug into 29.99, and in that formula since it's add/subtract, then it can be either R or F since they would cancel out and you are looking at the delta between the two:
Ns,comp = (T2-T1)/(T'2-T1) it's just a ration of the deltas, so as long as the T's are all in the same units, whether F or R, they should work. Still, goes back to it must be a requirement of equation 29.18 which needs to have absolute temp units?