A 65 kg hiker's metabolism supplies her 4.0 Mcal of energy in a day. Modeling the hiker as a Carnot heat engine operating between body temperature (37) and the temperature of the air (20), calculate the maximum height she can climb in one day.

a. Sketch the situation, defining all your variables.

b. What physics equation(s) will you utilize in order to solve this problem? For each equation you list, give a justification for why it applies to this situation.

c. Apply your equation(s) to solve the problem as an algebraic expression(s).

d. Calculate your numerical answer(s). Show the units of your answer(s), and how you got them.