Chapter 19: Problem 29
What measures may be taken to reduce the likelihood of thermal shock of a ceramic piece?
Chapter 19: Problem 29
What measures may be taken to reduce the likelihood of thermal shock of a ceramic piece?
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Get started for freeA 0.4-m (15.7-in.) rod of a metal elongates \(0.48\) \(\mathrm{mm}\left(0.019\right.\) in.) on heating from \(20^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\) \(\left(68^{\circ} \mathrm{F}\right.\) to \(\left.212^{\circ} \mathrm{F}\right)\). Determine the value of the linear coefficient of thermal expansion for this material.
We might think of a porous material as being a composite in which one of the phases is a pore phase. Estimate upper and lower limits for the room- temperature thermal conductivity of an aluminum oxide material having a volume fraction of \(0.25\) of pores that are filled with still air.
(a) Briefly explain why \(C_{v}\) rises with increasing temperature at temperatures near \(0 \mathrm{~K}\). (b) Briefly explain why \(C_{v}\) becomes virtually independent of temperature at temperatures far removed from \(0 \mathrm{~K}\).
The constant \(A\) in Equation \(19.2\) is \(12 \pi^{4} R / 5 \theta_{\mathrm{D}}^{3}\), where \(R\) is the gas constant and \(\theta_{\mathrm{D}}\) is the Debye temperature \((\mathrm{K})\). Estimate \(\theta_{\mathrm{D}}\) for aluminum, given that the specific heat is \(4.60 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) at \(15 \mathrm{~K}\).
A steel wire is stretched with a stress of 70 MPa \((10,000 \mathrm{psi})\) at \(20^{\circ} \mathrm{C}\left(68^{\circ} \mathrm{F}\right) .\) If the length is held constant, to what temperature must the wire be heated to reduce the stress to \(17 \mathrm{MPa}\) \((2500 \mathrm{psi}) ?\)
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