Neco 2022 Physics Question 8

Practice essay / theory question 8 from the 2022 Neco Physics examination. This question covers Thermal stress, Linear expansion, Young's modulus, Specific heat capacity, Heat transfer, Convection .

Neco 2022 Physics Essay / Theory
Topics: Thermal stress Linear expansion Young's modulus Specific heat capacity Heat transfer Convection
Question 8 NECO • 2022 • PHYSICS • essay

A solid cylindrical rod of steel has a length of 0.500 m, a diameter of 20 mm and a density of 7850 kg·m⁻³. The coefficient of linear expansion of steel is \(\alpha = 1.2\times10^{-5}\ \text{K}^{-1}\) and its Young's modulus is \(E = 2.0\times10^{11}\ \text{Pa}\). The rod is fixed at both ends so that it cannot expand when heated. The yield strength of the steel is 250 MPa. The specific heat capacity of steel is 470 J·kg⁻¹·K⁻¹. The rod is placed in a water bath at 25°C and heated uniformly. The convective heat‑transfer coefficient between the rod surface and the water is \(h = 150\ \text{W·m}^{-2}\text{K}^{-1}\). Assume the water temperature remains constant at 25°C throughout the heating process.

Question Parts

( a )
Derive the expression for the thermal stress developed in the rod when its temperature is raised by \(\Delta T\) while the ends remain fixed.
( b )
Calculate the temperature increase \(\Delta T_{yield}\) that would cause the thermal stress to reach the yield strength of the steel.
( c )
Determine the amount of heat energy \(Q\) required to raise the temperature of the rod by \(\Delta T_{yield}\).
( d )
If the rod is heated only by convection from the water bath, estimate the time required to supply the heat \(Q\) calculated in part (c). Assume the entire lateral surface of the rod participates in convection and neglect heat loss from the ends.

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About This Question

This is Neco 2022 Physics Question 8. It is one of the essay questions from the 2022 Neco Physics examination.

The question covers Thermal stress, Linear expansion, Young's modulus, Specific heat capacity, Heat transfer, Convection .

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