Solving Thermal Equilibrium Problem: Aluminum & Iron Rods

In summary, the conversation discusses a problem involving two rods made of different materials that are joined together and maintained at different temperatures. The goal is to determine the temperature at the interface between the two rods and the amount of energy conducted across them in a given time. The conduction equation is used to solve for the temperature, taking into account the different thermal conductivities of the two materials. Another problem involving a U-tube filled with water and oil is also discussed, with the goal of determining the difference in the heights of the two liquid surfaces and the speed of air being blown across one of the arms.
  • #1
JJMezzapesa
5
0
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 celcius, and the free end of the iron rod is maintained at 0 degrees celcius. (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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  • #2
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.
 
  • #3
how do you determine the temperature using the conduction equation when there are two different materials, thus two different thermal conductivity constants?
 
  • #4
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
 

FAQ: Solving Thermal Equilibrium Problem: Aluminum & Iron Rods

What is thermal equilibrium?

Thermal equilibrium is a state in which two objects or systems that are in contact with each other have reached the same temperature and there is no net transfer of heat between them.

What is the thermal conductivity of aluminum and iron?

The thermal conductivity of a material is a measure of its ability to conduct heat. The thermal conductivity of aluminum is 237 W/mK and the thermal conductivity of iron is 80.2 W/mK.

How do you solve a thermal equilibrium problem?

To solve a thermal equilibrium problem, you need to use the equation Q = mcΔT, where Q is the heat transfer, m is the mass of the object, c is the specific heat capacity of the material, and ΔT is the change in temperature. You also need to consider the thermal conductivity and surface area of the objects in contact.

What factors affect thermal equilibrium?

The factors that affect thermal equilibrium include the thermal conductivity of the objects, their surface area, the temperature difference between them, and the duration of contact.

How can I apply thermal equilibrium in real-life situations?

Thermal equilibrium is a fundamental concept in many real-life situations, such as cooking, heating and cooling systems, and thermal insulation. It is also used in industries such as metallurgy and engineering to ensure the proper functioning of machinery and equipment.

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