A pot with a steel bottom 8.50 mm thick rests on a hot stove. The area of the bottom of the pot

A pot with a steel bottom 8.50 mm thick rests on a hot...

A pot with a steel bottom 8.50 $\mathrm{mm}$ thick rests on a hot stove. The area of the bottom of the pot is 0.150 $\mathrm{m}^{2} .$ The water inside the pot is at $100.0^{\circ} \mathrm{C},$ and 0.390 $\mathrm{kg}$ are evaporated every 3.00 min. Find the temperature of the lower surface of the pot, which is in contact with the stove.

Key Concepts

Latent Heat of Vaporization

Latent heat of vaporization is the amount of energy required to convert a unit mass of a liquid into vapor without changing its temperature. This concept is critical in energy balance calculations, especially when phase changes like evaporation occur, which absorb large amounts of energy.

Energy Balance in Heat Transfer

Energy balance in heat transfer is the application of the conservation of energy principle, where the energy entering a system must equal the energy leaving the system plus any change in stored energy. In problems involving phase changes and conduction, this balance helps determine unknown parameters such as surface temperatures or required energy inputs.

Fourier’s Law

Fourier’s law is a fundamental relation in heat transfer that quantifies the conductive heat transfer rate. It states that the heat transferred per unit time is proportional to the negative temperature gradient and the cross-sectional area perpendicular to the flow of heat, and inversely proportional to the distance over which the temperature difference exists.

Thermal Conduction

Thermal conduction is the process by which heat energy is transmitted through collisions between neighboring atoms or molecules. In solids, this process is described by Fourier’s law, which relates the heat transfer rate to the temperature gradient, the area through which heat is flowing, and the material's thermal conductivity.

Thermal Conductivity

Thermal conductivity is a material property that measures the ability of a substance to conduct heat. It plays a crucial role in determining how quickly heat can pass through a material, which is essential in designing and analyzing systems involving heat transfer, such as heating elements and thermal insulators.

Transcript

00:01 All right guys, so we're looking for to figure out the temperature that is on the lower part, which is the part that attached the stove.

00:08 Okay, if we draw a picture, so this is the pot, okay, and there's a stove heating up, this is the fire, okay? that's the lower part we're looking for.

00:24 Okay, so for this kind of question, we can set out such an equation, which is h equal to k -a times th minus tc over l.

00:40 H is the heat currents, k is the thermoconductivity of the steel, a is the surface area, thh is the higher temperature, tc is the lower temperature, and l is the length, and in this case the thickness of the parts.

00:57 Okay, so we know that the thickness of the part is 8 .5 millimeter, which is a.

01:12 5 times 10 to the power of 93 meter.

01:17 Okay.

01:21 And th is the one we're looking for.

01:26 Because the temperature at a low part of the slope is obviously higher than a temperature inside of the pots because it touched the stove directly.

01:36 So we know the tc is equal to, so the low temperature is equal to 100 degrees celsius.

01:44 That's the temperature inside of our parts.

01:46 Okay.

01:49 Area is 0 .15 meter square.

01:58 Okay.

02:02 And the thermoconductivity is equal to 50 .2 watts per meter times kelvin.

02:17 Well, it seems that we don't know the heat currents, but the heat currents are simply the power, which is equal to the energy divide by time.

02:32 Okay.

02:34 So the energy we are using here, is actually the heat that was used to boil water...

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