Engineering, 27.05.2020 12:58, jwyapo4

An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at 1.0 wt%.

If after 50 h the concentration of carbon is 0.35 wt% at a position 3.5 mm below the surface, determine the temperature at which the treatment was carried out.

Answers: 3

Show answers

Answers

answered: montanolumpuy

the temperature T at which the treatment is carried is out is 1274.24 K

Explanation:

Fick's second Law posits that the rate of change of concentration of diffusing species is directly proportional to the second derivative of the concentration.

Using the expression of the Fick's second Law:

$\mathbf{\frac{C_x-C_o}{C_s-C_o} = 1- erf(\frac{x}{2\sqrt{Dt} })}$

where;

C_o = initial concentration

C_x = the depth of the concentration

C_s = surface concentration

$erf(\frac{x}{2\sqrt{Dt} })}$ = Gaussian error function.

Let variable z be used for the expression of the Gaussian error function. $erf(\frac{x}{2\sqrt{Dt} })}$

Then, from the above equation: replacing C_x with 0.35 ; C_o with 0.2 and C_s with 1.0; we have:

$\mathbf{\frac{0.35-0.2}{1.0-0.2} = 1- erf( z)}$

erf (z) = 0.8125

we obtain the error function value close to 0.8125 from the error function table and we did the interpolation to obtain the exact value of variable corresponding to 0.8125.

The table below shows the tabular form of the error function value close to 0.8125 .

Value for z Value for erf (z)

0.9 0.797

z 0.8125

0.950 0.8209

From above; we can find the value of variable corresponding to the error function 0.8125 .

i.e

$\frac{z-0.9}{0.95-0.9} =\frac{0.8125-0.797}{0.8209-0.797}$

z = 0.932

However, the temperature dependence relation for the diffusion coefficient D can be expressed as:

$z = \frac{x}{\sqrt{Dt} }$

where;

z = 0.932

x = 3.5 mm = 0.0035 m

t = 50 h = 180000 sec

$0.932 = \frac{0.35}{2\sqrt{D*180000} }$

D = $1.958*10^{-11} m^2/s$

Finally, the temperature T at which the treatment is carried is out is calculated as:

$\mathbf{D=D_o \ exp \ (-\frac{Q_d}{RT}) }$

From the table ‘Diffusion data’, we obtain the values of temperature-independent pre exponential and activation energy for diffusion of carbon in FCC Fe.

$D_o = 2.3*10^{-5} \ m^2/s$

$Q_d = 148, 000 \ J/mol$

Replacing all values needed for the above equation; we have:

$1.958*10^{-11}= (2.3*10^{-5})exp(\frac{-148,000}{(8.31)T})$

$8.51*10^{-7}=exp(\frac{-17,810}{T})$

$In(8.51*10^{-7})=(\frac{-17,810}{T})$

-13.977 = -17,810/T

T = -17,810/ - 13.977

T = 1274.24 K

Hence, the temperature T at which the treatment is carried is out is 1274.24 K

answered: Guest

answer:

explanation:

assault rifle is a rapid-fire, magazine-fed rifle designed for military use. it is a shoulder-fired weapon that allows the shooter to select between semi-automatic (requiring you pull the trigger for each shot), fully automatic (hold the trigger and the gun continuously fires) or three-shot-burst modes.

answered: Guest

answer:

explanation:

Other questions on the subject: Engineering

Engineering, 04.07.2019 18:10, anna22684

Water at 70°f and streams enter the mixing chamber at the same mass flow rate, determine the temperature and the quality of the exiting stream. 0 psia is heated in a chamber by mixing it with saturated water vapor at 20 psia. if both streams enters the mixing chamber at the same mass flow rate, determine the temperature and the quality of the existing system.

Answers: 2

continue

Engineering, 04.07.2019 18:10, redrosesxx

Water at 55c flows across a flat plate whose surface temperature is held constant at 95c. if the temperature gradient at the plate's surface for a given value of x is 18 c/mm, find a) local heat transfer coefficient. b) heat flux

Answers: 3

continue

Engineering, 04.07.2019 18:10, salazjlove

Which of the following refers to refers to how well the control system responds to sudden changes in the system. a)-transient regulation b)- distributed regulation c)-constant regulation d)-steady-state regulation

Answers: 1

continue

Engineering, 04.07.2019 18:10, wyattlb97

Water at the rate of 1 kg/s is forced through a tube with a 2.5 cm inner diameter. the inlet water temperature is 15°c, and the outlet water temperature is 50°c. the tube wall temperature is 14°c higher than the local water temperature all along the length of the tube. what is the length of the tube?

Answers: 3

continue

Do you know the correct answer?

An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature an...