1. Suppose you make a cup of tea with boiling water straight from a kettle, but then the phone rings and you are distracted so that you only find your cup of cold tea later in the day.
(a) Estimate the change in entropy of the room during the cooling of the tea.
(b) Prove that the change in entropy of the tea is mc ln(Tf / Ti) [This is a general expression for the change in entropy of any substance (with mass m and specific heat c) that is taken from an initial temperature Ti to a final temperature Tf. Hint: you need to do an integral.]
(c) Hence find a numerical value for the change in entropy of the tea. [Neglect the specific heat of the cup (and the tea bag), and assume the room remains at a constant temperature.]