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Snezhnost [94]
3 years ago
5

A 5.45-g combustible sample is burned in a calorimeter. the heat generated changes the temperature of 555 g of water from 20.5°c

to 39.5°c. how much energy is released by the burning? the specific heat of water is 4.18 j/ (°c × g). 564 j 2,500 j 44,100 j 138,000 j
Physics
1 answer:
Y_Kistochka [10]3 years ago
3 0
Given:
m = 555 g, the mass of water in the calorimeter
ΔT = 39.5 - 20.5 = 19 °C, temperature change
c = 4.18 J/(°C-g), specific heat of  water

Assume that all generated heat goes into heating the water.
Then the energy released is
Q = mcΔT
    = (555 g)*(4.18 J/(°C-g)*(19 °C)
    = 44,078.1 J
    = 44,100 J (approximately)

Answer:  44,100 J

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A closely wound, circular coil with a diameter of 4.30 cm has 470 turns and carries a current of 0.460 A .
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Hi there!

a)
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μ₀ = Permeability of free space (4π × 10⁻⁷ Tm/A)

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dB = \frac{\mu_0}{4\pi} \frac{id\vec{l}}{r^2}

Now, let's write the integral, replacing 'dl' with 'ds' for an arc length:
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Taking out constants from the integral:
B =\frac{\mu_0 i}{4\pi R^2}  \int ds

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B =\frac{\mu_0 i}{4\pi R^2}  \int\limits^{2\pi R}_0 \, ds

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Plugging in our givens to solve for the magnetic field strength of one loop:

B = \frac{(4\pi *10^{-7}) (0.460)}{2(0.0215)} = 1.3443 \mu T

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b)

Now, we have an additional component of the magnetic field. Let's use Biot-Savart's Law again:
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In this case, we cannot disregard the cross-product. Using the angle between the differential length and radius vector 'θ' (in the diagram), we can represent the cross-product as cosθ. However, this would make integrating difficult. Using a right triangle, we can use the angle formed at the top 'φ', and represent this as sinφ.  

dB = \frac{\mu_0}{4\pi} \frac{id\vec{l} sin\theta}{r^2}

Using the diagram, if 'z' is the point's height from the center:

r = \sqrt{z^2 + R^2 }\\\\sin\phi = \frac{R}{\sqrt{z^2 + R^2}}

Substituting this into our expression:
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B = \frac{\mu_0 iR}{4\pi (z^2 + R^2)^\frac{3}{2}}} \int\limits^{2\pi R}_0, ds

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Multiplying by the number of loops:
B_T= \frac{\mu_0 N iR^2}{2 (z^2 + R^2)^\frac{3}{2}}}

Plug in the given values:
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