1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
natita [175]
3 years ago
6

A common method to measure thermal conductivity of a biomaterial is to insert a long metallic probe axially into the center of a

long cylindrical container of the material. The probe is maintained at some uniform temperature Ti, and the outside of the container is maintained at a temperature To. Inside the metallic probe is an electrical heater for which the electrical power is measured. If the diameter of the probe maintained at 50°C is 1 cm, the outer diameter of the container maintained at 20°C is 4 cm, the length of the cylinder container is 60 cm, and the power input is 40.8 W, calculate the thermal conductivity of this material.
Physics
1 answer:
tia_tia [17]3 years ago
8 0

Answer:

The thermal conductivity of the biomaterial is approximately 1.571 watts per meter-Celsius.

Explanation:

Let suppose that thermal conduction is uniform and one-dimensional, the conduction heat transfer (\dot Q), measured in watts, in the hollow cylinder is:

\dot Q = \frac{2\cdot k\cdot L}{\ln \left(\frac{D_{o}}{D_{i}} \right)}\cdot (T_{i}-T_{o})

Where:

k - Thermal conductivity, measured in watts per meter-Celsius.

L - Length of the cylinder, measured in meters.

D_{i} - Inner diameter, measured in meters.

D_{o} - Outer diameter, measured in meters.

T_{i} - Temperature at inner surface, measured in Celsius.

T_{o} - Temperature at outer surface, measured in Celsius.

Now we clear the thermal conductivity in the equation:

k = \frac{\dot Q}{2\cdot L\cdot (T_{i}-T_{o})}\cdot \ln\left(\frac{D_{o}}{D_{i}} \right)

If we know that \dot Q = 40.8\,W, L = 0.6\,m, T_{i} = 50\,^{\circ}C, T_{o} = 20\,^{\circ}C, D_{i} = 0.01\,m and D_{o} = 0.04\,m, the thermal conductivity of the biomaterial is:

k = \left[\frac{40.8\,W}{2\cdot (0.6\,m)\cdot (50\,^{\circ}C-20\,^{\circ}C)}\right]\cdot \ln \left(\frac{0.04\,m}{0.01\,m} \right)

k \approx 1.571\,\frac{W}{m\cdot ^{\circ}C}

The thermal conductivity of the biomaterial is approximately 1.571 watts per meter-Celsius.

You might be interested in
The aqueduct passes under Johnson Road in Lancaster through a siphon. The maximum capacity of the aqueduct is 350 m3/s. The heig
Mariulka [41]

Answer:

D ≈ 8.45 m

L ≈ 100.02 m

Explanation:

Given

Q = 350 m³/s (volumetric water flow rate passing through the stretch of channel, maximum capacity of the aqueduct)

y₁ - y₂ = h = 2.00 m (the height difference from the upper to the lower channels)

x = 100.00 m (distance between the upper and the lower channels)

We assume that:

  • the upper and the lower channels are at the same pressure (the atmospheric pressure).
  • the velocity of water in the upper channel is zero (v₁ = 0 m/s).
  • y₁ = 2.00 m  (height of the upper channel)
  • y₂ = 0.00 m  (height of the lower channel)
  • g = 9.81 m/s²
  • ρ = 1000 Kg/m³ (density of water)

We apply Bernoulli's equation as follows between the point 1 (the upper channel) and the point 2 (the lower channel):

P₁ + (ρ*v₁²/2) + ρ*g*y₁ = P₂ + (ρ*v₂²/2) + ρ*g*y₂

Plugging the known values into the equation and simplifying we get

Patm + (1000 Kg/m³*(0 m/s)²/2) + (1000 Kg/m³)*(9.81 m/s²)*(2 m) = Patm + (1000 Kg/m³*v₂²/2) + (1000 Kg/m³)*(9.81 m/s²)*(0 m)

⇒ v₂ = 6.264 m/s

then we apply the formula

Q = v*A  ⇒   A = Q/v ⇒   A = Q/v₂

⇒   A = (350 m³/s)/(6.264 m/s)

⇒   A = 55.873 m²

then, we get the diameter of the pipe as follows

A = π*D²/4   ⇒   D = 2*√(A/π)

⇒   D = 2*√(55.873 m²/π)

⇒   D = 8.434 m ≈ 8.45 m

Now, the length of the pipe can be obtained as follows

L² = x² + h²

⇒ L² = (100.00 m)² + (2.00 m)²

⇒ L ≈ 100.02 m

6 0
3 years ago
Read 2 more answers
What is refraction of light?
prohojiy [21]

Answer:

bending of light

Explanation:

6 0
3 years ago
Read 2 more answers
g The electric power needs of a community are to be met by windmills with 40-m-diameter rotors. The windmills are to be located
Ksenya-84 [330]

Answer:

Explanation:

Given Data

The diameter of the wind mills is d = 40m

Velocity of the air is V = 6 m / s

Required power output is:  P ₀ = 2100 k W

Expression to calculate the exergy of the air is

E = V ² / 2

Substitute the value in above expression

E = ( 6 m / s ) ² / 2

E = 18 m ² / s ² x (1kJ/kg / 1000m²/s²)

E = 0.018 k J / k g

Expression to calculate the density of the air is

P v =m R T

m /v = P  /RT ⋯ ⋯( I )

Here  

m  is the mass of the air,  

v  is the volume of the air,  

P  is the atmospheric pressure,  

T  is the standard temperature at the atmospheric pressure and  

R  is the gas constant

As the density is

ρ = m /V

Substitute the value in expression (I)

ρ = 101  kP a /( 0.287 k J / k g ⋅ K ) ( 298 K )

ρ = 1.180 k g / m ²

Expression to calculate the mass flow rate is

m = ρ A V ⋯ ⋯ ( I I )

Here  A  is the area of the windmill

Expression to calculate the  A  is

A = π /4  d ²

Substitute the value in above expression

A = π /4 ( 40 m ²)

A = 1256.63 m ²

Substitute the value in expression (II)

m = ( 1.180 k g / m ³) ( 1256.63 m ²) ( 6 m / s )

m = 8896.94  k g / s

Expression to calculate the maximum power available to the windmill is

P w = m ( V ² /2 )

Substitute the value in above expression

P w = 8896.94  k g / s ( (6m/s)²/2 )

P w = 160144.92 W  × ( 1 W /1000 k W )

P w = 160.144 k W

Expression to calculate the number of windmills required is

n = P o /P w

Substitute the value in above expression

n=2100kw/160.144kw

n=13.11

8 0
3 years ago
How to do this question
mestny [16]

thanks again and have to go to the store and get some rest I will be there at puno my phone is not working and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about the week and I have a few questions about you

4 0
2 years ago
Which statement accurately describes something that Yolanda can do as a part of her study?
Vikki [24]
Thank you for posting your question here at brainly. Below is Yoland's study:

<span>Yolanda is studying two waves. The first wave has an amplitude of 2 m, and the second has an amplitude of 3 m.
</span>
I think the answer is "She can use constructive interference to generate a wave with an amplitude of 1.5 m."
6 0
3 years ago
Read 2 more answers
Other questions:
  • How and why has the Atomic Theory changed over time
    12·1 answer
  • Difference between xrays and radio wave
    7·1 answer
  • Sonar is a device that uses reflected sound waves to measure underwater depths. If a sonar signal has a frequency of 288 Hz and
    6·1 answer
  • What's true about the elliptical path that the planets follow around the sun? A. A line can be drawn from the planet to the sun
    10·1 answer
  • In a lab experiment, two identical gliders on an air track are held together by a piece of string, compressing a spring between
    11·1 answer
  • How much time does it take for a car with a speed of 85 m/s to drive a distance of 200 m? (1 point)
    15·1 answer
  • What would be the most accurate way to describe resistance?
    12·2 answers
  • PLEASE HELP!!! GIVING BRAINLIEST!! ill also answer questions that you have posted if you answer this correctly!!!! (50pts)
    10·1 answer
  • Compare and contrast the solar eclipse seen in this video to a lunar eclipse.
    14·1 answer
  • What is the work required to raise a 20 Newton box from the surface of the earth to a height of 6 meters?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!