Solving Thermal Equilibrium Problem: Aluminum & Iron Rods

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Homework Help Overview

The discussion revolves around a thermal equilibrium problem involving an aluminum rod and an iron rod in thermal contact, with specified temperatures at their ends. Participants are exploring how to determine the interface temperature and the energy conducted across the rods over a set time period. Additionally, another participant introduces a separate problem involving fluid dynamics in a U-tube with water and oil.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • The original poster attempts to understand the thermal equilibrium setup and seeks guidance on applying the conduction equation. Some participants question how to account for differing thermal conductivities of the materials involved. Another participant introduces a different problem related to fluid heights and air motion, prompting questions about the relationship between fluid dynamics and pressure differences.

Discussion Status

The discussion is ongoing, with participants raising questions about the application of thermal conduction principles and the complexities introduced by different materials. There is an exploration of the concepts involved, but no consensus or resolution has been reached yet.

Contextual Notes

Participants are navigating the constraints of the problems, including the need to consider different thermal conductivities and the effects of air motion on fluid levels in the U-tube scenario. The original poster expresses difficulty in understanding the thermal equilibrium problem, indicating a potential gap in foundational knowledge.

JJMezzapesa
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I have been trying to figure this problem out for a while now and get stuck everytime. I do not understand how to go about it. Any help would be greatly appriciated.

An aluminum rod and an iron rod are joined end to end in good thermal contact. The two rods have equal lengths and radii. The free end of the aluminum rod is maintained at a temperature of 100 degrees celsius, and the free end of the iron rod is maintained at 0 degrees celsius. (a) Determine the temperature of the interface between the two rods. (b) If each rod is 15 cm long and each has a cross-sectional area of 5.0 cm2(squared), what quantity of energy is conducted across the combination in 30 minutes?
 
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Thermal equilibrium means the heat transfer dQ/dt is constant at all cross-sections. Apply the conduction equation at the interface for aluminum and iron.
 
how do you determine the temperature using the conduction equation when there are two different materials, thus two different thermal conductivity constants?
 
I do not understand this problem either.

A U-TUBE AT BOTH ENDS IS PARTIALLY FILLED WITH WATER. OIL (DENSITY = 750KG/M2) IS THEN POURED INTO THE RIGHT ARM AND FORMS A COLUMN L=5.00 CM HIGH. DETERMINE THE DIFFERENCE h IN THE HEIGHTS OF THE TWO LIQIUD SURFACES. THE RIGHT ARM IS THEN SHIELDED FROM ANY AIR MOTION WHILE AIR IS BLOWN ACROSS THE TOP OF THE LEFT ARM UNTIL THE SURFACES OF THE TWO LIQUIDS ARE AT THE SAME HEIGHT. DETERMINE THE SPEED OF OF THE AIR BEING BLOWN ACROSS THE LEFT ARM. ASSUME THE DENSITY OF AIR IS 1.29 KG/M2
 

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