a) Conversion from Fahrenheit to Celsius:
The relationship between the two scales is the following
[tex]T_f = \frac{9}{5}T_c + 32 [/tex]
where
[tex]T_f[/tex] is the temperature in Fahrenheit
[tex]T_c[/tex] is the temperature in Celsius
Re-arranging the formula, we find the inverse relationship:
[tex]T_c= \frac{5}{9}(T_f-32) [/tex]
and we can use this equation to convert [tex]T_f = 89.3^{\circ}F[/tex] into Celsius:
[tex]T_c = \frac{5}{9}(89.3-32)=31.7^{\circ} C [/tex]
(b) Conversion to Kelvin scale:
The conversion between Celsius scale and Kelvin scale is easier:
[tex]T_k = T_c + 273.1[/tex]
where [tex]T_k [/tex] is the temperature in Kelvin. Using [tex]T_c = 31.7^{\circ} C[/tex], we find
[tex]T_k = 31.7 + 273.1 = 304.8 K[/tex]
