In an attempt to save money to compensate for a budget shortfall, it has been determined that the steam in ChE Hall will be shut down at 6:00 P.M. and turned back on at 6:00 A.M., much to the chagrin of a busy class of chemical engineers who have an outrageously long computer project due the following day. The circulation fans will stay on, however, leaving the entire building at approximately the same temperature. Well, things aren’t going as quickly as you might have hoped and it is getting cold in the computer lab. You look at your watch; it is already 10:00 P.M. and the temperature has already fallen halfway from the comfortable 22ºC it was maintained at during the day to the 2ºC of the outside temperature (i.e., the temperature is 12ºC at 10:00 P.M.). Seeing as you will probably be there all night and you need a diversion, you decide to estimate what the temperature will be at 6:00 A.M. You may assume the outside temperature stays constant at 2ºC from 6:00 P.M. to 6:00 A.M. You may take the heat transfer to be given by the following expression:

where h is a constant.
(a) Plot what you think the temperature will be as a function of time. Explain.
(b) Calculate the temperature at 6:00 A.M.

Transcribed Image Text:

q=h(T-Tsurr)