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ehidna [41]
3 years ago
6

For a cylindrical annulus whose inner and outer surfaces are maintained at 30 ºC and 40 ºC, respectively, a heat flux sensor mea

sures the magnitude of the heat flux at 3cmr= as 40 W/m2. Assume that the temperature distribution is steady and depends only on the radial coordinate. Under the hypothesis that the thermal conductivity is independent of temperature, what is k if a) the inner and outer radii
Engineering
1 answer:
miskamm [114]3 years ago
7 0

Answer:

k=0.12\ln(r_2/r_1)\frac {W}{ m^{\circ} C}

where r_1 and r_2 be the inner radius, outer radius of the annalus.

Explanation:

Let r_1, r_2 and L be the inner radius, outer radius and length of the given annulus.

Temperatures at the inner surface, T_1=30^{\circ}C\\ and at the outer surface, T_2=40^{\circ}C.

Let q be the rate of heat transfer at the steady-state.

Given that, the heat flux at r=3cm=0.03m is

40 W/m^2.

\Rightarrow \frac{q}{(2\pi\times0.03\times L)}=40

\Rightarrow q=2.4\pi L \;W

This heat transfer is same for any radial position in the annalus.

Here, heat transfer is taking placfenly in radial direction, so this is case of one dimentional conduction, hence Fourier's law of conduction is applicable.

Now, according to Fourier's law:

q=-kA\frac{dT}{dr}\;\cdots(i)

where,

K=Thermal conductivity of the material.

T= temperature at any radial distance r.

A=Area through which heat transfer is taking place.

Here, A=2\pi rL\;\cdots(ii)

Variation of temperature w.r.t the radius of the annalus is

\frac {T-T_1}{T_2-T_1}=\frac{\ln(r/r_1)}{\ln(r_2/r_1)}

\Rightarrow \frac{dT}{dr}=\frac{T_2-T_1}{\ln(r_2/r_1)}\times \frac{1}{r}\;\cdots(iii)

Putting the values from the equations (ii) and (iii) in the equation (i), we have

q=\frac{2\pi kL(T_1-T_2)}{\LN(R_2/2_1)}

\Rightarrow k= \frac{q\ln(r_2/r_1)}{2\pi L(T_2-T_1)}

\Rightarrow k=\frac{(2.4\pi L)\ln(r_2/r_1)}{2\pi L(10)} [as q=2.4\pi L, and T_2-T_1=10 ^{\circ}C]

\Rightarrow k=0.12\ln(r_2/r_1)\frac {W}{ m^{\circ} C}

This is the required expression of k. By putting the value of inner and outer radii, the thermal conductivity of the material can be determined.

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klasskru [66]

Answer:

a) Check explanation for this

b)Rate law is  Rate = \frac{k_{1}k_{4}  }{k_{3}+ 2k_{4}  } [H_{2} ]

c) The rate does not depend on the concentration of CO₂

Explanation:

a) Elementary steps for the RWGS reaction:

  • Dissociative adsorption of the H₂ Molecule

                 H_{2} $\xrightarrow{\text{k1}}$H + H   (Fast process)

  • Reversible Reaction between CO₂ and H

                \[ CO_{2} + H\mathrel{\mathop{\rightleftarrows}^{\mathrm{k2}}_{\mathrm{k3}}}COOH \] (Fast Process)

  • Slow dissociation of COOH into gaseous CO and absorbed OH

                COOH $\xrightarrow{\text{k1}}$ CO + OH (Slow process)

  • Fast hydrogenation of the OH to form H₂O

                   OH + H $\xrightarrow{\text{k5}}$H_{2} O (Fast process)

b) Derivation of the rate law

We need to determine the rate law for H, OH and COOH because these are the intermediates for this reaction.

The steady state approximation is applied to a consecutive reaction with a slow first step and a fast second step (k1≪k2). If the first step is very slow in comparison to the second step, there is no accumulation of intermediate product.

Rate of consumption = Rate of production

For COOH:

Using steady state approximation

\frac{d[COOH]}{dt} = 0

k_{2} [CO_{2} ][H] = k_{3} [COOH] k_{4} [COOH]\\

[COOH] = \frac{k_{2} [CO_{2} ][H]}{k_{3}k_{4}  } \\

For H:

\frac{d[H]}{dt} = 0

k_{1}[H_{2}] = k_{2}[CO_{2} [H]+k_{5} [ OH][H]

[H]= \frac{k_{1}[H_{2}]  }{k_{5}[OH] +k_{2}[CO_{2}]}\\

For OH:

\frac{d[OH]}{dt} = 0

k_{4} [COOH] = k_{5} [OH][H]\\\k[OH] = \frac{k_{4} [COOH]}{k_{5} H}\\

The rate of the overall reaction is determined by the slowest step of the reaction. The slowest process is the dissociation of COOH

Therefore the overall rate of reaction is:

Rate = k_{4} [COOH]\\

Rate = k_{4}  \frac{k_{2} [CO_{2} ][H]}{k_{3}k_{4}  }\\Rate = k_{4}  \frac{k_{2}[CO_{2}]\frac{k_{1}[H_{2}]  }{k_{5}[OH] +k_{2}[CO_{2}]}  }{k_{3}k_{4}}\\Rate = k_{4}  \frac{k_{2}[CO_{2}]\frac{k_{1}[H_{2}]  }{k_{5}\frac{k_{4}COOH }{k_{5}H }  +k_{2}[CO_{2}]}  }{k_{3}k_{4}}

Simplifying the equation above, the rate law becomes

Rate = \frac{k_{1}k_{4}  }{k_{3}+ 2k_{4}  } [H_{2} ]

c) It is obvious from the rate law written above that the rate of the RWBG reaction does not depend on the concentration of CO₂

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What do you think the top TWO game elements are that directly contribute to player immersion?
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Sound (like music and background sound) and detail. The music and background sound is what sets the mood for the game. In horror games, the sound is sometimes uneasy to make the player feel anxious, and when something chases you the music turns into fast-pace and making the player scared and feel that adrenaline. The detail also is a great factor. The more realistic a game is, the more it feels like real life and determines if the player will get a real reaction from the game.
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2 years ago
A heat recovery system​ (HRS) is used to conserve heat from the surroundings and supply it to the Mars Rover. The HRS fluid loop
blagie [28]

Answer:

0.304 L of Freon is needed

Explanation:

Q = mCT

Q is quantity of energy that must be removed = 47 BTU = 47×1055.06 = 49587.82 J

C is specific heat of Freon = 74 J/mol.K = 74 J/mol.K × 1 mol/120 g = 0.617 J/g.K

T is temperature in the area of Mars = 189 K

m = Q/CT = 49587.82/(0.617×189) = 452.23 g = 452.24/1000 = 0.45223 kg

Density of Freon = specific gravity of Freon × density of water = 1.49 × 1000 kg/m^3 = 1490 kg/m^3

Volume of Freon = mass/density = 0.45223/1490 = 0.000304 m^3 = 0.000304×1000 = 0.304 L

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A civil engineer is studying a left-turn lane that is long enough to hold seven cars. Let X be the number of cars in the line at
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Answer:

a) C= 1/120

b) P(X>=5) = 0.333

Explanation:

The attached file contains the explanation for the answers

7 0
3 years ago
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If a vacuum gau ge reads 9.62 psi, it means that: a. the very highest column of mercury it could support would be 19.58 inches.
scZoUnD [109]

Answer:All of the above

Explanation:

9.62 psi means 497.49 mm of Hg pressure

for (a)19.58 inches is equals to 497.49 mm of Hg

(b)atmospheric pressure is 14.69 psi

vaccum gauge is 9.62psi

absolute pressure is=14.69-9.62=5.07

(c)vaccum means air is sucked and there is negative pressure so it tells about below atmospheric pressure.

thus all are correct

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3 years ago
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