A perfectly insulated enclosure containing a heater is filled with a liquid havi

Question

A perfectly insulated enclosure containing a heater is filled with a liquid having thermal capacitance C. The temperature of the liquid is assumed to be uniform and is denoted by theta. The heat supplied by the heater is q(t). a) write the differential equation obeyed by the liquid temperature theta. b) solve the equation you found in part (a) for theta in terms of the arbitrary initial temperature theta(0). c) sketch theta versus t when q_i(t) = 1 for 10 < t < or equal 20 and zero otherwise

Explanation / Answer

Consider the differential equation

where k is a positive constant. The solution of this differential equation is

This differential equation describes the heating or cooling of an object in a room whose temperature is a constant 70 degrees. This is the reason that the constant k must be positive. Since the function T(t) has two constants we expect to be able to satisfy two conditions. The purpose of this set of problems is to investigate this statement -- "we expect to be able to satisfy two conditions."

Notice that your answers to the five questions above depend on whether you require the constant k to be positive.

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