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Studentka2010 [4]
3 years ago
7

Carbon is allowed to diffuse through a steel plate 11 mm thick. The concentrations of carbon at the two faces are 0.88 and 0.41

kg C/m3 in Fe, which are maintained constant. If the preexponential and activation energy are 6.2 × 10-7 m2/s and 80,000 J/mol, respectively, compute the temperature (in K) at which the diffusion flux is 6.4 × 10-10 kg/m2-s. Enter your answer in accordance to the question statement K.
Physics
1 answer:
Serhud [2]3 years ago
8 0

Answer:

The temperature is 2584.5 K

Explanation:

Given:

Activation energy Q = 80000 \frac{J}{mol}

Preexponential D= 6.2 \times 10^{-7} \frac{m^{2} }{s}

Diffusion flux J = 6.4 \times 10^{-10} \frac{kg}{m^{2} s}

Thickness of plate \Delta x =  11 \times 10^{-3} m

Concentration of carbon at two faces \Delta C = (0.88 - 0.41 ) = 0.47 \frac{kg}{m^{3} }

From the formula of temperature in terms of diffusion flux,

  T = (\frac{Q}{R} ) \frac{1}{\ln (\frac{D\Delta C}{J\Delta x} )}

Where R = 8.314 \frac{J}{mol.K} ( gas constant )

Put the values and find the temperature,

  T = (\frac{80000}{8.314} ) \frac{1}{\ln (\frac{6.2 \times 10^{-7} \times 0.47 }{6.4 \times 10^{-10}\times 11 \times 10^{-3} } )}

  T = 2584.5 K

Therefore, the temperature is 2584.5 K

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