Question

Assume a cup contains about 12 oz or 340 g of water at room temperature, about 20 degree C. The electric kettle draws energy from the wall outlet at a rate (Power) of 990W. Draw a single Energy-Interaction Diagram for the process of bringing the water to a rolling boil. Choose an appropriate physical system, as well as an initial and a final point in time and indicate all initial and final conditions on your timeline. Explicitly state any other assumptions you're making in words (incl. observations) and include an energy-conservation equation. Use your energy-conservation equation to calculate the amount of energy necessary to bring the water to a rolling boil. Then use what you know about the power of the electric kettle to calculate how long it will take to bring the water to a rolling boil (all water in liquid/gas mixed state).

Answer 1

The energy diagram would be like the following:

Using first law of thermodynamics:

Since there is no work in this system, then internal energy change is equal to heat. And under steady-state conditions, the electric power is the income energy to the system, then:

Using the concept of sensible heat:

This is a simple first-order differential equation with initial condition of temperature of 20°C at t=0. Replacing the given data:

Solving the equation:

This shows that temperature varies lineraly with time. Assuming that boiling point is at T=100°C, then, time to get this point is:

As known, after getting boiling point, the substance states at a isothermal process until all the mass converts from fluid to gas (latent heat with a fluid7gas mixture). After this, the gas will increase again its temperature. Then, we can define a temperature functions as:

after this point, temperature states constan (till all the fluid is converted into gas). If we make a T vs. t graph (the end of fluid/gas mixture is not determined in the context of the problem):