P1: A kettle (mass = 0.9 kg) made of aluminum is filled with 600 g water, both the kettle and the water
are at a temperature of 25 oC.
a. If 100 g of ice (0 oC) is added to the water, what would be the final temperature of the kettle
and water (assume no heat loss to the pad or evaporation)?
b. After the temperature steadies, the kettle is transferred onto a pre-heated stovetop (140 oC).
What is the initial rate of energy transfer if the bottom of the kettle is 0.3 cm thick and has a
diameter of 10 cm?
c. How much energy is required to boil away all of the water?
To answer these questions, we need to use the principles of heat transfer and energy conservation. Let's go through each question step by step:
a. To find the final temperature of the kettle and water after adding ice, we need to consider the heat exchanged between the system components.
First, we calculate the heat transferred between the ice and the water when the ice melts:
Q1 = m1 * Lf
where m1 is the mass of the ice (100 g) and Lf is the latent heat of fusion for water (334,000 J/kg).
Next, we calculate the heat transferred from the water to the kettle:
Q2 = m2 * cw * (Tf - Ti)
where m2 is the mass of the water (600 g), cw is the specific heat capacity of water (4,186 J/kg°C), Tf is the final temperature, and Ti is the initial temperature (25°C).
Finally, we equate the heat transferred from the ice to the heat transferred to the kettle and water:
Q1 = Q2
Now we can solve for the final temperature Tf.
b. To find the initial rate of energy transfer to the kettle when it is placed on the pre-heated stovetop, we need to calculate the heat flux.
The heat flux through the bottom of the kettle is given by:
q = (k * (T1 - T2)) / L
where q is the heat flux, k is the thermal conductivity of aluminum (205 W/m·K), T1 is the temperature of the stovetop (140°C), T2 is the initial temperature of the kettle and water, and L is the thickness of the kettle bottom (0.3 cm).
The initial rate of energy transfer is the product of the heat flux and the surface area of the bottom of the kettle.
c. To find the amount of energy required to boil away all the water, we need to calculate the heat transferred during boiling.
The heat transferred during boiling can be calculated using the formula:
Q = m * Lv
where Q is the heat transferred, m is the mass of water (600 g), and Lv is the latent heat of vaporization for water (2,260,000 J/kg).
So, to find the answer to each question, follow the steps outlined above and plug in the given values and constants into the respective formulas.