8. A car travels at a constant velocity of 70 mph for one hour. By the end of the second hour, the car’s velocity was 60 mph. At
1 answer:
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Part 1) Which metal will cool the fastest?
To answer this question, we should have a look at the formula of the heat flow rate, which says "how fast" a material is able to heat/cool:
where:
is the heat exchanged
is the time interval
k is thermal conductivity of the material
A the surface where the exchange of heat occurs
the variation of temperature
x is the thickness of the material
We see that the heat flow rate
is linearly proportional to k, the thermal conductivity of the material. So, the larger k, the fastest the metal will cool.
If we have a look at the thermal conductivity of each metal, we find:
- Aluminium: 237 W/(mK)
- Copper: 401 W/(mK)
- Gold: 314 W/(mK)
- Platinum: 69 W/(mK)
Therefore, copper is the material with highest heat flow rate, so the metal which cools fastest.
Part 2) Which sample of copper demonstrates the greatest increase in temperature
To solve this part, we can have a look at how the amount of heat exchanged Q is related to the increase in temperature:
where m is the mass and Cs the specific heat of the material. Re-arranging the formula, we get
therefore, we see that the increase in temperature is inversely proportional to the mass m. This means that the block that will show the largest increase in temperature is the block with the smallest mass, so the correct answer is A) 0.5 kg.
To answer this question, we should have a look at the formula of the heat flow rate, which says "how fast" a material is able to heat/cool:
where:
k is thermal conductivity of the material
A the surface where the exchange of heat occurs
x is the thickness of the material
We see that the heat flow rate
If we have a look at the thermal conductivity of each metal, we find:
- Aluminium: 237 W/(mK)
- Copper: 401 W/(mK)
- Gold: 314 W/(mK)
- Platinum: 69 W/(mK)
Therefore, copper is the material with highest heat flow rate, so the metal which cools fastest.
Part 2) Which sample of copper demonstrates the greatest increase in temperature
To solve this part, we can have a look at how the amount of heat exchanged Q is related to the increase in temperature
where m is the mass and Cs the specific heat of the material. Re-arranging the formula, we get
therefore, we see that the increase in temperature is inversely proportional to the mass m. This means that the block that will show the largest increase in temperature is the block with the smallest mass, so the correct answer is A) 0.5 kg.
Answer:
C = 2.9 10⁻⁵ F = 29 μF
Explanation:
In this exercise we must use that the voltage is
V = i X
i = V/X
where X is the impedance of the system
in this case they ask us to treat the system as an RLC circuit in this case therefore the impedance is
X =
tells us to take inductance L = 0.
The angular velocity is
w = 2π f
the current is required to be half the current at high frequency.
Let's analyze the situation at high frequency (high angular velocity) the capacitive impedance is very small
→0 when w → ∞
therefore in this frequency regime
X₀ =
the very small fraction for which we can despise it
X₀ = R
to halve the current at f = 200 H, from equation 1 we obtain
X = 2X₀
let's write the two equations of inductance
X₀ = R w → ∞
X= 2X₀ = w = 2π 200
we solve the system
2R = \sqrt{R^2 +( \frac{1}{wC} )^2 }
4 R² = R² + 1 / (wC) ²
1 / (wC) ² = 3 R²
w C =
C =
let's calculate
C =
C = 2.9 10⁻⁵ F
C = 29 μF