Answer:
Tt = 70 + 135e^-0.031t
13 minutes
Explanation:
Given that :
Initial temperature, Ti = 205°
Temperature after 2.5 minutes = 195°
Temperature of room, Ts= 70
Using the relation :
Tt = Ts + Ce^-kt
Temperature after time, t
When freshly poured, t = 0
205 = 70 + Ce^-0k
205 = 70 + C
C = 205 - 70 = 135°
T after 2.5 minutes to find proportionality constant, k
Tt = Ts + Ce^-kt
195 = 70 + 135e^-2.5k
125 = 135e^-2.5k
125 / 135 = e^-2.5k
0.9259 = e^-2.5k
Take In of both sides :
−0.076989 = - 2.5k
k = −0.076989 / - 2.5
k = 0.031
Equation becomes :
Tt = 70 + 135e^-0.031t
t when Tt = 160
160 = 70 + 135e^-0.031k
90 = 135e^-0.031t
90/135 = e^-0.031t
0.6667 = e^-0.031t
In(0.6667) = - 0.031t
−0.405465 = - 0.031t
t = 0.405465/ 0.031
t = 13.071
t = 13 minutes
The velocity of the ball is 12.5 m/s
Explanation:
The velocity of the ball is given by the ratio between the distance covered by the ball and the time taken:
First, we calculate the distance covered. We know that the radius of the circle is
r = 0.450 m
And the length of the circumference is
The ball makes 25.0 revolutions, so a total distance of
In a time of
t = 9.37 s
So, its velocity is
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Answer:
15.8 V
Explanation:
The relationship between capacitance and potential difference across a capacitor is:
where
q is the charge stored on the capacitor
C is the capacitance
V is the potential difference
Here we call C and V the initial capacitance and potential difference across the capacitor, so that the initial charge stored is q.
Later, a dielectric material is inserted between the two plates, so the capacitance changes according to
where k is the dielectric constant of the material. As a result, the potential difference will change (V'). Since the charge stored by the capacitor remains constant,
So we can combine the two equations:
and since we have
V = 71.0 V
k = 4.50
We find the new potential difference:
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Answer: Option (B) is the correct answer.
Explanation:
Convection is defined as a process in which a fluid (liquid or gas) is heated and the cooler liquid (more dense) settles or sinks at the bottom whereas a hotter material (less dense) will rises to the top.
For example, ice being less dense (cooler material) will float in a lake whereas liquid water being more dense will sink at the bottom.
Thus, we can conclude that situation in which convection currents most likely occur is within the water in a lake as ice forms on the top.
