Ethylene glycol is the main component in automobile antifreeze. To monitor the temperature of an auto cooling system, you intend to use a meter that reads from 0 to 100. You devise a new temperature scale based on the approximate melting and boiling points of a typical antifreeze solution (-45^οC and 115^οC). You wish these points to correspond to 0^οA and 100^οA, respectively.

a. Derive an expression for converting between ^οA and ^οC.

b. Derive an expression for converting between ^οF and ^οA.

c. At what temperature would your thermometer and a Celsius thermometer give the same numerical reading?

d. Your thermometer reads 86^οA. What is the temperature in ^οC and in ^οF?

e. What is a temperature of 45^οC in ^οA?