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3 years ago

By using the principle of dimensional consistency, what is the correct dimension for thermal conductivity in the SI?

Physics

1 answer:

MAVERICK [17]3 years ago

8 0

Answer:

Explanation:

from Fourier law,

q = -K(∆T/L)

but q = Q/A,

hence,

K = (QL)/(AΔT)

Q = Joules/s = ML²/T³

L = L

A = L²

∆T = Kelvin = K

since K = (QL)/(AΔT)

substitute the fundamental units into the above equation we have

K = (ML²/T³)(L)/(L²K) = ML³/T³L²K = ML/T³K

the thermal conductivity, K dimensionality = ML/T³K

or mass lenght per cube unit seconds per Kelvin

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3 years ago

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3 years ago

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Two vectors are illustrated in the coordinate plane.

oksano4ka [1.4K]

Answer: (-4.3, 2.5)

Explanation:

In the second quadrant, magnitude of the vector is 5 and angle is 30° from the negative x-axis.

We can write this in terms of its components:

$-5 cos 30^o \hat i + 5 sin 30^o\hat j$

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Thus, the components of vector in the second quadrant are (-4.3, 2.5)

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3 years ago

An aluminum sphere is 8.55 cm in diameter. What will be it's % change in volume if it is heated from 30 C to 155 C?

Ghella [55]

We know that

• The sphere diameter is 8.55 cm.

• The temperature change is from 30 C to 155 C.

First, we have to find the radius of the sphere. The radius is the half diameter.

$\begin{gathered} r=\frac{d}{2}=\frac{8.55\operatorname{cm}}{2} \\ r=4.275\operatorname{cm} \end{gathered}$

Now we have to find the volume of the sphere using the following formula.

$V=\frac{4}{3}\pi(r)^3$

Where r = 4.275 cm.

$\begin{gathered} V=\frac{4}{3}\pi(4.275\operatorname{cm})^3 \\ V\approx327.26(cm)^3 \end{gathered}$

Then, we use the following formula

$V_2-V_1=BV_0(T_2-T_1)$

Where the initial volume is 327.26 cubic cm, B is a constant about thermal expansion for aluminum, and we have to find the final volume to then calculate the percentage change.

$\begin{gathered} \Delta V=75\times10^{-6}\cdot327.26(155-30) \\ \Delta V=75\times10^{-6}\cdot327.26(125) \\ \Delta V\approx3.07(cm)^3 \end{gathered}$

This means that the volume change is 3.07 cubic centimeters.

At last, we have to divide the volume change by the initial volume, and then we have to multiply it by 100% to express it as a percentage.

$\frac{\Delta V}{V_1}\times100=\frac{3.07}{327.26}\times100\approx0.938$ <h2>Therefore, the percentage change is 0.938%.</h2>

5 0

1 year ago

While an object is moving at a constant 20 m/s, a 5 N forcepushes the object to the left. At the same time, a 5 N force ispushin

Nostrana [21]

Answer: 20m/s.

Explanation:

Remember the second Newton's law:

F = a*m

This is:

The net force acting on an object is equal to the mass of the object times the acceleration of the object.

In this case, we have a force of 5N pushing the object to the right.

We also have a force of 5N pushing the object to the left.

These forces act on opposite directions.

Then the net force will be equal to the difference of these forces, this is:

F = 5N - 5N = 0N

Then the net force is 0N, then we have:

0N = m*a

0N/m = 0m/s^2 = a

This means that the acceleration of the object is 0, then the velocity of the object does not change.

This means that if the object was moving at a constant velocity of 20m/s, the velocity of the object will still be equal to 20m/s. (because the net force acting on the object is zero)

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3 years ago