The carburizing time necessary to achieve a carbon concentration is 31.35 hours
<h3>How to find the Carburizing Time?</h3>
To determine the carburizing time necessary to achieve the given carbon concentration, we will use the equation:
(Cs - Cx)/(Cs - C0) = ERF(x/2√Dt)
where;
Cs is Concentration of carbon at surface = 0.90
Cx is Concentration of carbon at distance x = 0.30
Distance x = 4 mm = 0.004 m
C0 is Initial concentration of carbon = 0.10
ERF() = Error function at the given value
D = Diffusion of Carbon into steel
t = Time necessary to achieve given carbon concentration ,
Thus, plugging in the relevant values gives;
(Cs - Cx)/(Cs - C0) = (0.9 - 0.3)/(0.9 - 0.1)
= 0.6/0.8 = 0.75
now, ERF(z) = 0.75 and as such using ERF table, we can say that;
Z = 0.814. Thus;
(x/2√Dt) = 0.81
Using the table of diffusion data, we have;
At a temperature of (1100°C) or 1373 K, we have;
D = 5.35 × 10⁻¹¹ m²/sec.
Calculating the carbonizing time by using the equation z = (x/2√Dt);
where;
t is carbonizing time
Thus;
0.814 = (0.004/(2 × √5.35 × 10⁻¹¹ × √t))
0.814 = 0.004 /(1.4628 × 10⁻⁵ × √t)
0.814 × 1.4628 × 10⁻⁵ × √t = 0.004
1.19072 × 10⁻⁵ × √t = 0.004
√t = 0.004/(1.19072 × 10⁻⁵)
√t = 335.93
t = 112848.96 seconds
Converting to hours gives;
t = 112848.96/3600
t = 31.35 hours
Therefore, the carburizing time necessary to achieve a carbon concentration is 31.35 hours
Read more about Carburizing Time at; brainly.com/question/13031810
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