Basic Thermodynamics ~ J. Pohl © www.THERMOspokenhere.com

When will the Teapot Whistle?

Suppose you pour 1 liter of water into a thermally insulated, electrically heated teapot then you turn it on. The label on the teapot states that in operation, it draws 1250 Watts of power. The metal of the teapot has a thermal equivalent equal 200 cm³ of water.
i)What is the very shortest time you will have to wait before the water boils and for pot begins to whistle?
ii)Assume you get so involved in your thermo homework that you forget to pull the plug on the kettle, once started, for how long will whistling of the teapot continue?

Discussion and Solution:  We take the system to be the water and the metal. We begin by writing the energy equation in a first, implicit, or skeletal form. There are three terms. At any instance in time, the rate change of energy (of the water and teapot) equals the sum of work rates applicable plus the sum of heat rates applicable. The implicit equation for these materials as they sit on the table and as they operate (once initiated) is :

 (1)(1)

Below left, the energy term, E, for the sake of beginners, is expanded to its internal energy, kinetic energy and potential energy components. Also, right-of-equality, the sum of works term, ΣW-dot is expanded.

 (2)(2)

Where

(i)  represents the rate of change of the internal energy of the pot materials and of the water it contains.

(ii)  represents the "possibility" of kinetic and/or potential energy change of the center of mass of the water or teapot materials. These are zero, of course; the pot does not move, the water (that that boils) moves slowly.

(iii)  Work attends events for which a system (or its components) expands (or contracts). The water experiences expansion. The pot does also but only very slightly.

(iv)  this term represents whatever work might have occurred that caused a change of kinetic or potential energy of the water and/or pot. For this case this is zero.

(v)  one way to treat electrical resistance heating is to consider it to be electric work done on the system.

(vi)  as heating of the water and pot occur, the temperature increase of the substances (above their initial ambient temperature) will provide an incentive for heat from the system to the surroundings. This, being very hard to calculate, is ignored with first calculations (and included later if necessary).

We arrive at a new equation:

 (3)(3)

By striking (i) and (ii) in the above equation to be zero, we have ignored (approximated) the teapot to deliver All of the EE directly to the water while retaining none for itself.

The remaining term, (3) left-of-equality, and the first term, right-of-equality, combine to be enthalpy for water.

 (4)(4)

 (5)(5)

 (6)(6)

When will the Teapot Whistle?

When you turn it on, a thermally insulated, electrically heated teapot pour contains 1 liter of water at @25°C. The metal of the teapot is equivalent to 200 cubic centimeters of water and the label of the teapot says it is rated at 1250 W. How long will you have to wait for the water to boil and for the pot to whistle?