1. A person eats 2,000 calories per day, has a skin temperature of 35C, and performs a negligible amount of work on their surroundings compared to how much food they eat. Assume the average ambient temperature is 295 K. a) Calculate the maximum rate of useful work, in Watts, that could theoretically be extracted from this person by a heat engine. One food calorie (one kilocalorie) equals 4187 Joules. b) The battery in the iPhone 13 Pro can store 41 kJ of energy. How long would it take to fully charge the phone, in hours, using the power calculated in part (a)? c) Direct sunlight carries a thermal energy flux of 1 kW/m. Calculate the edge length, in cm, of the theoretically smallest possible square of area that could be used to produce as much useful work from direct sunlight as can be extracted from the person in part (a). The effective surface temperature of the Sun is 5778 K. d) The average temperature of the cosmic microwave background (CMB) radiation in deep space is 2.7 K. Would a Carnot heat engine built into the space suit of an astronaut lost in deep space (operating between Tskin and TCMB) be more or less efficient than a Carnot heat engine based on Earth operating on direct sunlight?