# Thermal Conductivity Problem-- Two Reservoirs

• Kara4566
In summary, the question is asking for the entropy change of the water-steam mixture, not the entropy change of the overall combined system.
Kara4566
Suppose that a large mixture of ice and water is in thermal contact with a reservoir which contains a large quantity of water and steam. Assume that both the ice/water bath and the water/steam reservoirs are otherwise thermally isolated and at a constant temperature. The only contact between them is via a uniform rod which is made of a conductive metal and has a uniform cross-sectional area. The latent heat for the ice-water transition is 3.3×105 J kg , and the latent heat for the water-steam transition is 2.26×106 J kg .

Suppose that the rate of energy transport is 450W, that the thermal conductivity of the metal is 210 W m K , and that the rod is square with a side-length of 0.14m. What is the length of the rod?

What is the change in entropy of the water/steam mixture during a period where 1200J of energy is transported from the water/steam mixture to the ice/water mixture?The unknown variable I seem to require to solve both of the above questions is the temperature change between the reservoirs. Is there a way to find the temperature change using the latent heats given? I have attempted these problems numerous times but still, am not successful in finding the temperatures of the reservoirs. Are the temperatures even necessary to solve the problems? Any help is greatly appreciated!

What temperature can water exist as both a solid (ice) and liquid at the same time?

Also think about the other phase state - gas (steam) alongside liquid water.

Kara4566
P=(Tsteam-Tice)*K*W*W/L
450=100*210*0.14*0.14/L
L=0.915m

entropy change is dH/Tice - dH/Tsteam = 1200/273 - 1200/373 = 4.396 - 3.217 = 1.179 J/K

Kara4566
trurle said:
P=(Tsteam-Tice)*K*W*W/L
450=100*210*0.14*0.14/L
L=0.915m

entropy change is dH/Tice - dH/Tsteam = 1200/273 - 1200/373 = 4.396 - 3.217 = 1.179 J/K

Thank you very much! Makes sense.

As to whether you need to know the temperature difference, take a look at the dimensions of what you are given. Specifically, the thermal conductivity relates Power (Energy/Time) and Length and Temperature.

trurle said:
P=(Tsteam-Tice)*K*W*W/L
450=100*210*0.14*0.14/L
L=0.915m

entropy change is dH/Tice - dH/Tsteam = 1200/273 - 1200/373 = 4.396 - 3.217 = 1.179 J/K
The question asks for the entropy change of the water-steam mixture, not the entropy change of the overall combined system.

Chestermiller said:
The question asks for the entropy change of the water-steam mixture, not the entropy change of the overall combined system.
But should the solution be even posted at all... right off the bat? The OP had not even a chance to attempt it. His original question was asking how to determine the temperatures of the two reservoirs.

scottdave said:
But should the solution be even posted at all... right off the bat? The OP had not even a chance to attempt it. His original question was asking how to determine the temperatures of the two reservoirs.
I think some gave the member a Warning for this.

Chestermiller said:
I think some gave the member a Warning for this.
That makes sense. I recall doing something similar when I was new.

scottdave said:
That makes sense. I recall doing something similar when I was new.
Who doesn't. Guilty too.

## 1. What is thermal conductivity?

Thermal conductivity is the measure of a material's ability to conduct heat. It is the rate at which heat energy is transferred through a material from a higher temperature to a lower temperature.

## 2. What is the "Thermal Conductivity Problem-- Two Reservoirs"?

The "Thermal Conductivity Problem-- Two Reservoirs" is a theoretical problem in which two reservoirs at different temperatures are connected by a material with a known thermal conductivity. The problem involves calculating the rate of heat transfer between the two reservoirs.

## 3. How is thermal conductivity measured?

Thermal conductivity is typically measured in units of watts per meter kelvin (W/mK). It can be measured using various techniques, such as the hot wire method or the guarded hot plate method.

## 4. What factors affect thermal conductivity?

The thermal conductivity of a material is affected by various factors, including temperature, density, and moisture content. It also depends on the type of material and its physical properties, such as its molecular structure and the presence of impurities.

## 5. Why is thermal conductivity important?

Thermal conductivity is an important property in various fields, including engineering, physics, and materials science. It helps in understanding and predicting heat transfer in different systems, such as buildings, electronics, and industrial processes. It also plays a crucial role in the design and optimization of thermal insulation materials.

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