A pot of mushroom soup taken from a microwave oven at 96'C and a jug of apple juice taken from a refrigerator at 4"C are put on a dinner table. The temperature in the dining room is held at 22"C. After 10 minutes, the soup temperature is 52 C and the juice temperature is 15-C, (a) Find km, the proportionality constant for the mushroom soup, Now find ka for the apple juice. (3 marks) (b) How long will it take the soup to lose its taste quality, i.e., to cool down to the temperature of 32"C? What is the juice temperature at this moment? (3 marks) (c) Assuming that km for the soup does not change, when would the soup reach 32'C if it was left on a table of an outside cafe on a hot summer day when the temperature is 30"C? Why are the results so different from the ones obtained in part (b)