There are numerous methods to estimate the temperature of substances. Some say it is possible to estimate the temperature of air in degrees Fahrenheit by counting the number of chirps a cricket makes...

There are numerous methods to estimate the temperature of substances. Some say it is possible to estimate the temperature of air in degrees Fahrenheit by counting the number of chirps a cricket makes in 15 seconds, then adding that number to 37.Consider a new temperature scale based on the rate that crickets chirp. Assume that the temperature in this scale is equal to the number of times a cricket chirps per minute and that the temperature on this scale is reported as °X.

(a) Derive an expression that relates temperature in degrees Fahrenheit (T°F)to degrees Cricket (T°X).

(b) Given that the heat capacity of blood at body temperature is 1.87J/(g.°F),what is the heat capacity of blood at body temperature in J/(g.°X)?

(c)The heat capacity of blood as a function of temperature is given by:

Derive an equation for the heat capacity of blood that uses temperature in °X and gives the heat capacity in J/(g.°X). In other words, determine what the numerical values are for the constants a and b in the following equation:

(d)To check that your answer in part (c) is correct, calculate the heat capacity of blood at 98.6°F using both equations and compare the results. Do the results of your calculations make sense?