Question 4: Newton's Law of Cooling/ Warming A cold apple juice taken from a frigerator and placed on a table in a room rmalt ire main up to the temperature of the urrounding air. A very hot mushroom soup removed from a microwave and placed on the same table cools down to the temperature of the surrounding In situations like these, the rate at which an object's temperature is changing at any given time is approximately proportional to the difference between its temperature and the temperature of the surrounding medium. This observation is sometimes called the Newton's Law of Cooling, although, as in the case with the apple juice, it applies to warming as well. An equation representing this law for the apple juice is given by T() -T, - (T - T, je -4, where I (t ) is the temperature of the object at time t (in minutes), T, is the surrounding constant temperature, To is the temperature of the object when : = 0 and k, is the proportionality constant for the apple juice. Similarly, for the mushroom soup, we have T(!) - T, - (To -The where km is the proportionality constant for the mushroom soup **"Where necessary, round your results to 4 decimal places,* ** A pot of mushroom soup taken from a microwave oven at 96 0 and a jug of apple juice taken from a refrigerator at 4C 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 0 and the juice temperature is 15"C. (a) Find km, the proportionality constant for the mushroom soup. Now, find k. for the apple juice. (3 marks) (b ) How long will it take the soup to lose its taste quality, be., to cool down to the temperature of 32"C? What is the juice temperature at this moment marks) (c) Assuming that k., 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 07 Why are the results so different from the ones obtained in part (b )