A thin layer of 316 stainless steel ( = 16.0 x 10-6 (oC)-1, E = 193 GPa) is cladded on a thick block of 1025 steel ( = 12.0 x 10-6 (oC)-1, E = 207 GPa). When operated at 500oC, what stress would occur to the 316 stainless steel cladded layer? Assume no residual stress after the cladding process.

cNo stress occur

A bar of copper is heated to 30 C and then placed into a Styrofoam cup of water. Thermal equilibrium between the copper bar and water is reached at 40 C. What was the temperature of the water before the copper bar was dropped into it? Why?

aLess than 40 C because copper can hold more heat than water.
bLess than 40 C because the copper bar heated the water.
cGreater than 40 C because water can hold more heat than copper.
dGreater than 40 C because the water heated the copper bar.
eGreater than 40 C because the water and copper bar would cool down on their own without interacting with each other or anything else.


Question 1: Stress in the 316 Stainless Steel Cladded Layer

The stress that would occur in the 316 stainless steel cladded layer is a tensile stress.

Here’s why:

  1. Different Thermal Expansion Coefficients: The coefficient of thermal expansion (CTE) of 316 stainless steel is higher than that of 1025 steel. This means that when heated, the stainless steel will expand more than the 1025 steel.
  2. Cladding Restraint: Since the cladded layer is thin and bonded to the thicker 1025 steel block, it cannot expand freely. This constraint will cause the stainless steel to stretch, inducing a tensile stress.
  3. Temperature Increase: As the operating temperature increases to 500°C, the difference in expansion between the two materials will be amplified, leading to a higher tensile stress in the stainless steel.

Therefore, due to the different thermal expansion coefficients and the constraint imposed by the cladding process, the 316 stainless steel cladded layer will experience a tensile stress when operated at 500°C.

Question 2: Temperature of Water before the Copper Bar

The temperature of the water before the copper bar was dropped into it was less than 40°C.

Here’s why:

  1. Heat Transfer: When the hot copper bar is placed in the water, heat will transfer from the copper to the water. This is because the copper has a higher temperature than the water, and heat naturally flows from hot objects to colder objects.
  2. Equilibrium Temperature: As the heat transfer continues, the temperature of the copper will decrease while the temperature of the water will increase. This process will continue until both substances reach thermal equilibrium, where their temperatures are equal.
  3. Heat Capacity: Since the copper bar has a smaller heat capacity than the water, it will lose its heat faster than the water gains heat. Therefore, the equilibrium temperature will be closer to the initial temperature of the water than the initial temperature of the copper.

Therefore, based on the principles of heat transfer and heat capacity, the water must have been colder than 40°C before the copper bar was introduced. The specific temperature difference depends on the initial temperatures of both substances, their respective heat capacities, and the amount of heat transferred.

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