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Nitella [24]
4 years ago
12

Calculate the diffusion coefficient for magnesium in aluminum at 500oC. Pre-exponential and activation energy values for this sy

stem are 1.2 x 10-4m2/s and 144,000 J/mole respectively. R = 8.314 J/mol K
Engineering
1 answer:
slega [8]4 years ago
7 0

Answer:

The diffusion coefficient for magnesium in aluminum at the given conditions is 2.22x10⁻¹⁴m²/s.

Explanation:

The diffusion coefficient represents how easily a substance (solute, e.g.: magnesium) can move through another substance (solvent, e.g.: aluminum).

The formula to calculate the diffusion coefficient is:

D=D₀.exp(- EA/R.T)

Each term of the formula means:

D: diffusion coefficient

D₀: Pre-exponential factor (it depends on each particular system, in this case the magnesium-aluminium system)

EA: activation energy

R: gas constant

T: temperature

1st) It is necessary to make a unit conversion for the temperature from °C to K, because we need to solve the problem according to the units of the gas constant (R) to assure the units consistency, so:

Temperature conversion from °C to K: 500 + 273 = 773 K

2nd) Replace the terms in the formula and solve:

D=D₀.exp(- EA/R.T)

D=1.2x10⁻⁴m²/s . exp[- 144,000 J/mole / (8.314 J/mol K . 773K)]

D=1.2x10⁻⁴m²/s . exp(-22.41)

D=1.2x10⁻⁴m²/s . 1.85x10⁻¹⁰

D= 2.22x10⁻¹⁴m²/s

Finally, the result for the diffusion coefficient  is 2.22x10⁻¹⁴m²/s.

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A spherical, stainless steel (k 16 W m1 K-1) tank has a wall thickness of 0.2 cm and an inside diameter of 10 cm. The inside sur
SOVA2 [1]

Answer:

the rate of heat loss is 2.037152 W

Explanation:

Given data

stainless steel K = 16 W m^{-1}K^{-1}

diameter (d1) = 10 cm

so radius (r1)  = 10 /2 = 5 cm = 5 × 10^{-2}

radius (r2)  = 0.2 + 5 = 5.2 cm = 5.2 × 10^{-2}

temperature = 25°C

surface heat transfer coefficient = 6 6 W m^{-2}K^{-1}

outside air temperature = 15°C

To find out

the rate of heat loss

Solution

we know current is pass in series from temperature = 25°C to  15°C

first pass through through resistance R1  i.e.

R1  = ( r2 -  r1 ) / 4\pi  × r1 × r2 × K

R1  = ( 5.2 - 5 ) 10^{-2}  / 4\pi  × 5 × 5.2 × 16 × 10^{-4}

R1  = 3.825 ×  10^{-3}

same like we calculate for resistance R2 we know   i.e.

R2 = 1 / ( h × area )

here area = 4 \pi r2²

area = 4 \pi (5.2 × 10^{-2})²  =  0.033979

so R2 = 1 / ( h × area ) = 1 / ( 6 × 0.033979  )

R2 = 4.90499

now we calculate the heat flex rate by the initial and final temp and R1 and R2

i.e.

heat loss = T1 -T2 / R1 + R2

heat loss = 25 -15 / 3.825 ×  10^{-3} + 4.90499

heat loss =  2.037152 W

8 0
3 years ago
g A food department is kept at -12oC by a refrigerator in an environment at 30oC. The total heat gain to the food department is
boyakko [2]

Answer:

a) \dot W = 0.417\,kW, b) COP_{R} = 2.198, c) Irreversible.

Explanation:

a) The power input required by the refrigerator is:

\dot W = \dot Q_{H} - \dot Q_{L}

\dot W = \left(4800\,\frac{kJ}{h} - 3300\,\frac{kJ}{h}\right)\cdot \left(\frac{1}{3600} \,\frac{h}{s} \right)

\dot W = 0.417\,kW

b) The Coefficient of Performance of the refrigerator is:

COP_{R} = \frac{\dot Q_{L}}{\dot W}

COP_{R} = \frac{3300\,\frac{kJ}{h} }{(0.417\,kW)\cdot \left(3600\,\frac{s}{h} \right)}

COP_{R} = 2.198

c) The maximum ideal Coefficient of Performance of the refrigeration is given by the inverse Carnot's Cycle:

COP_{R,ideal} = \frac{T_{L}}{T_{H}-T_{L}}

COP_{R,ideal} = \frac{261.15\,K}{303.15\,K - 261.15\,K}

COP_{R,ideal} = 6.218

The refrigeration cycle is irreversible, as COP_{R} < COP_{R,ideal}.

3 0
3 years ago
PLZZZZZ HELP
Makovka662 [10]

Answer:

As you might imagine, people working in robotics have strong mathematics, science, programming, and systems analysis skills. But design also plays a big role. Being able to iterate, isolate problems, and prototype until you have just the right design is essential.

Explanation:

hope that helps

6 0
3 years ago
Read 2 more answers
A metal having a cubic structure has a density of , an atomic weight of , and a lattice parameter of Å One atom is associated wi
Veronika [31]

Answer:

Explanation:

Answer: The crystal structure of the metal is BCC

Explanation:

we first calculate the volume of the unit cell.

Volume of unit cell= (a°)^3.

The lattice parameter here is a°.

Substitute (6.13 * 10^-8)cm for a°.

Volume of unit cell = (6.13 * 10^-8)^3 = 2.3034 * 10^-22 cm^3/cell.

To determine the crystal structure we use

Density (p) = {(Number of atoms per cell) (Atomic mass)} / {(volume of unit cell)(Avogrado constant)}.

Substitute 1.892g/cm^3 for p (6.02*10^23) atoms/mol for Avogrado constant 1.3921g/mol.

For atomic mass and (2.3034 * 10^-22) cm^3/cell for unit cell.

1.892g/cm^3 = {(Number of atoms per cell) (1.3291g/mol)} / {(2.3034 * 10^-22) (6.02 * 10^23 atoms/mol)}.

Changing the subject of formula we have :

Number of atoms per cell = {(2.3034 * 10^-22) * (6.02 * 10^23) * 1.892} / 132.91

Number of atoms per cell = 2.

Since the number of atoms per cell is 2, :. the crystal structure of metal is BCC.

Note: p = density

a° = a subscript o

4 0
3 years ago
Carbon dioxide used as a natural refrigerant flows through a cooler at 10 MPa, which is supercritical, so no condensation occurs
kupik [55]

Answer:

The answer which is a calculation can be found as an attached document

Explanation:

5 0
3 years ago
Read 2 more answers
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