Question

Pd and Au have complete solid solubility at all temperatures and compositions. Adding 20 wt.%Pd to Au increases the solidus temperature from 1064˚ C to 1250˚ C, which is hot enough to allow an Al₂O₃-based ceramic veneer to be fired at 1200˚ C around a Au-20Pd alloy stump for a dental implant. The coefficient of thermal expansion of this ceramic is 7.3 x 10^-6 C˚^-1.

(a) Use the rule of mixtures to estimate the coefficient of thermal expansion of the Au-20Pd alloy.

(b) The Au-Pd stump is a solid, 3mm diameter cylinder with a roughened surface to assure strong bonding to the ceramic. Assuming the ceramic-metal interface remains well bonded during cooling to room temperature, will the ceramic veneer have a residual tensile or compressive hoop stress near the ceramic-metal interface?

Answer 1

Sautione Given that coefficient of the Thermal expansion of this ceramic is 7:34 10 ben * Ceramic veneer to be fixed = 12000 Temperature -1066°C to 12.50°c flw --Pav To find. 4, then the rate at which the Internal Energy of the gay is changing in terms of pand A. * If we compress gay at constantert * presswa pest' such Of Atmospheric e pressure 'peth such af Atmospheric * Pressure we obtain is wa-Pav * When the volume change by small amount for a Small Change in volume do, the work is do=_PAV * where the amount of Energy dul is then du= dw= apdy 'n Idris added to the system. The Expression for work . When the volume is constant though out then the pressur change and Internal Energy is then Au: Wafter- U before * A sequence of small volume and energy change from Vaffer to sum up the work Ausq fuis constant] .

So, when heat is removed from the System q'is Negative and Jalu-gao * The sum of heat and work is they always equal to the Total Internal change in the sysem lau=qtw] * work Energy is Tram fer due to change in the External macroscopic variably and that directely affect the macwscopic value 14:9460 a b) considering a moving particle towards the piston. 3 # let the component of ity Velocity per perpendicular to the Piston bevi * Assuming that the particle bounces of the piston Elastically, what is the Velocity of Perpendicular to the piston. Collession of Piston. At the Piston g= y(t) when we have Y = |(7) then CYCT) O, VIT)Ticycp)-0,2 W ()) fer v<w(7) and TT CY() -0, , ) (469) +0, 2017)) for U >w(1)

* where V Represents the Velorita olor collision moung and 20 (P) & that before collision here WCT) = y(a) is the Velocity of piston * pistong Velocity remains to describe the evoluation of (T). - * suppose the pistory at Time'l is ay and its ve locity 'w. * The piston is affected by the peuticle (YU) hitting it from the right (such that y=y to and usw) * The Velocity of piston must satisfy the equation Sevil ft (10, up) ou - jens orcy to, du whereas acuits, Y,W):) Ti (Y40,41) if uw (acho, VIP) if/?w Apply the Integrals on both side and weget Ścu.worl)? synco-wcp) ) q[uip, yct)) When t so then | W() = Jun (49, UiT) IN JUTCH UP) От с 1-%, v) du Jт сно, от The component of Pty Velocity perpendicular to the Piston after colnsion. * Please give RATE', if help fun, Thank you *