Explanation Given Information: Depth, X = 0.05 in = 1.27 cm. Initial value of C, C 0 = 0.10% Value of C at X = Cx = 0.50% Constant surface carbon = Cs = 0.95% - 1.15% (consider max value) Calculation: According to Fick's equation, C s − C x C s − C o = e r f ( x 2 D t ) Here, Cs = Constant concentration Cx = Concentration of depth x C 0 = Initial concentration Putting values in equation, 0.0115 − 0.005 0.0115 − 0.001 = e r f ( 0.127 2 D t ) D t = 0.0635 0.6035 c m D t = 0.0011 c m 2 -------------------- (1) Now, calculate diffusion constant D, D = D 0 exp ( − Q R T ) Where, R = Gas constant = 1.987 cal/mol k Q = Activation energy = 33000 D 0 = Initial diffusion constant = 0.023 cm 2 D = 0.023 exp ( − 33000 1.987 × T ) ------------------------- (2) Combining equation (1) and (2), t = 0.048 exp ( − 16607 T ) Assuming some temperature to get combinations of temperatures and corresponding times. (1) T = 900 0 C = 1173 K t = 0.048 exp ( − 16607 1173 ) = 0

Essentials Of Materials Science And Engineering

4th Edition

ISBN: 9781337385497

Author: WRIGHT, Wendelin J.

Publisher: Cengage,

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Question

Chapter 5, Problem 5.83DP

Interpretation Introduction

Interpretation:

Carburizing heat treatment for steel gear needs to be designed.

Concept introduction:

Carburizing or case hardening is a process which develops wear resistant surface keeping toughness and strength of the core constant the Fick's second law and carbon concentration is required to find the value of time.

Expert Solution & Answer

Chapter 5 Solutions

Essentials Of Materials Science And Engineering

Ch. 5 - Prob. 5.1P Ch. 5 - Prob. 5.2P Ch. 5 - Prob. 5.3P Ch. 5 - Prob. 5.4P Ch. 5 - Prob. 5.5P Ch. 5 - Prob. 5.6P Ch. 5 - Prob. 5.7P Ch. 5 - Prob. 5.8P Ch. 5 - Prob. 5.9P Ch. 5 - Prob. 5.10P

Ch. 5 - Prob. 5.11P Ch. 5 - Prob. 5.12P Ch. 5 - Prob. 5.13P Ch. 5 - Prob. 5.14P Ch. 5 - Prob. 5.15P Ch. 5 - Prob. 5.16P Ch. 5 - Prob. 5.17P Ch. 5 - Prob. 5.18P Ch. 5 - Prob. 5.19P Ch. 5 - Prob. 5.20P Ch. 5 - Prob. 5.21P Ch. 5 - Prob. 5.22P Ch. 5 - Prob. 5.23P Ch. 5 - Prob. 5.24P Ch. 5 - Prob. 5.25P Ch. 5 - Prob. 5.26P Ch. 5 - Prob. 5.27P Ch. 5 - Prob. 5.28P Ch. 5 - Prob. 5.29P Ch. 5 - Prob. 5.30P Ch. 5 - Prob. 5.31P Ch. 5 - Prob. 5.32P Ch. 5 - Prob. 5.33P Ch. 5 - Prob. 5.34P Ch. 5 - Prob. 5.35P Ch. 5 - Prob. 5.36P Ch. 5 - Prob. 5.37P Ch. 5 - Prob. 5.38P Ch. 5 - Prob. 5.39P Ch. 5 - Prob. 5.40P Ch. 5 - Prob. 5.41P Ch. 5 - Prob. 5.42P Ch. 5 - Prob. 5.43P Ch. 5 - Prob. 5.44P Ch. 5 - Prob. 5.45P Ch. 5 - Prob. 5.46P Ch. 5 - Prob. 5.47P Ch. 5 - Prob. 5.48P Ch. 5 - Prob. 5.49P Ch. 5 - Prob. 5.50P Ch. 5 - Prob. 5.51P Ch. 5 - Prob. 5.52P Ch. 5 - Prob. 5.53P Ch. 5 - Prob. 5.54P Ch. 5 - Prob. 5.55P Ch. 5 - Prob. 5.56P Ch. 5 - Prob. 5.57P Ch. 5 - Prob. 5.58P Ch. 5 - Prob. 5.59P Ch. 5 - Prob. 5.60P Ch. 5 - Prob. 5.61P Ch. 5 - Prob. 5.62P Ch. 5 - Prob. 5.63P Ch. 5 - Prob. 5.64P Ch. 5 - Prob. 5.65P Ch. 5 - Prob. 5.66P Ch. 5 - Prob. 5.67P Ch. 5 - Prob. 5.68P Ch. 5 - Prob. 5.69P Ch. 5 - Prob. 5.70P Ch. 5 - Prob. 5.71P Ch. 5 - Prob. 5.72P Ch. 5 - Prob. 5.73P Ch. 5 - Prob. 5.74P Ch. 5 - Prob. 5.75P Ch. 5 - Prob. 5.76P Ch. 5 - Prob. 5.77P Ch. 5 - Prob. 5.78P Ch. 5 - Prob. 5.79P Ch. 5 - Prob. 5.80P Ch. 5 - Prob. 5.81DP Ch. 5 - Prob. 5.82DP Ch. 5 - Prob. 5.83DP Ch. 5 - Prob. 5.84DP Ch. 5 - Prob. 5.85DP Ch. 5 - Prob. 5.86CP Ch. 5 - Prob. 5.87CP Ch. 5 - Prob. 5.88CP Ch. 5 - Prob. K5.1KP

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