Answer:
PE = (|accepted value – experimental value| \ accepted value) x 100%
Explanation:
The height risen by water in the bell after enough time has passed for the air to reach thermal equilibrium is 3.8 m.
<h3>Pressure and temperature at equilibrium </h3>
The relationship between pressure and temperature can be used to determine the height risen by the water.
![\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}](https://tex.z-dn.net/?f=%5Cfrac%7BP_1V_1%7D%7BT_1%7D%20%3D%20%5Cfrac%7BP_2V_2%7D%7BT_2%7D)
where;
- V₁ = AL
- V₂ = A(L - y)
- P₁ = Pa
- P₂ = Pa + ρgh
- T₁ = 20⁰C = 293 K
- T₂ = 10⁰ C = 283 k
![\frac{PaAL}{T_1} = \frac{(P_a + \rho gh)A(L-y)}{T_2} \\\\\frac{PaL}{T_1} = \frac{(P_a + \rho gh)(L-y)}{T_2} \\\\L-y = \frac{PaLT_2}{T_1(P_a + \rho gh)} \\\\y = L (1 - \frac{PaT_2}{T_1(P_a + \rho gh)})\\\\y = 4.2(1 - \frac{101325 \times 283}{293(101325\ +\ 1000 \times 9.8 \times 100)} )\\\\y = 3.8 \ m](https://tex.z-dn.net/?f=%5Cfrac%7BPaAL%7D%7BT_1%7D%20%3D%20%5Cfrac%7B%28P_a%20%2B%20%5Crho%20gh%29A%28L-y%29%7D%7BT_2%7D%20%5C%5C%5C%5C%5Cfrac%7BPaL%7D%7BT_1%7D%20%3D%20%5Cfrac%7B%28P_a%20%2B%20%5Crho%20gh%29%28L-y%29%7D%7BT_2%7D%20%5C%5C%5C%5CL-y%20%3D%20%5Cfrac%7BPaLT_2%7D%7BT_1%28P_a%20%2B%20%5Crho%20gh%29%7D%20%5C%5C%5C%5Cy%20%3D%20L%20%281%20-%20%5Cfrac%7BPaT_2%7D%7BT_1%28P_a%20%2B%20%5Crho%20gh%29%7D%29%5C%5C%5C%5Cy%20%3D%204.2%281%20-%20%5Cfrac%7B101325%20%5Ctimes%20283%7D%7B293%28101325%5C%20%20%2B%5C%20%201000%20%5Ctimes%20%209.8%20%5Ctimes%20%20100%29%7D%20%29%5C%5C%5C%5Cy%20%3D%203.8%20%5C%20m)
Thus, the height risen by water in the bell after enough time has passed for the air to reach thermal equilibrium is 3.8 m.
The complete question is below:
A diving bell is a 4.2 m -tall cylinder closed at the upper end but open at the lower end. The temperature of the air in the bell is 20 °C. The bell is lowered into the ocean until its lower end is 100 m deep. The temperature at that depth is 10°C. How high does the water rise in the bell after enough time has passed for the air to reach thermal equilibrium?
Learn more about thermal equilibrium here: brainly.com/question/9459470
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Answer:
v = 3200 m/s
Explanation:
As we know that the frequency of the sound wave is given as
![f = 400 Hz](https://tex.z-dn.net/?f=f%20%3D%20400%20Hz)
wavelength of the sound wave is given as
![\lambda = 8 m](https://tex.z-dn.net/?f=%5Clambda%20%3D%208%20m)
so now we have
![speed = wavelength \times frequency](https://tex.z-dn.net/?f=speed%20%3D%20wavelength%20%5Ctimes%20frequency)
so we will have
![v = (8m) \times (400 Hz)](https://tex.z-dn.net/?f=v%20%3D%20%288m%29%20%5Ctimes%20%28400%20Hz%29)
![v = 3200 m/s](https://tex.z-dn.net/?f=v%20%3D%203200%20m%2Fs)
To solve the exercise it is necessary to take into account the definition of speed as a function of distance and time, and the speed of air in the sound, as well
![v=\frac{d}{t}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bd%7D%7Bt%7D)
Where,
V= Velocity
d= distance
t = time
Re-arrange the equation to find the distance we have,
d=vt
Replacing with our values
![d= (343)(3.7)](https://tex.z-dn.net/?f=d%3D%20%28343%29%283.7%29)
![d= 1269.1m](https://tex.z-dn.net/?f=d%3D%201269.1m)
It is understood that the sound comes and goes across the entire lake therefore, the length of the lake is half the distance found, that is
![L_{lake} = \frac{d}{2}](https://tex.z-dn.net/?f=L_%7Blake%7D%20%3D%20%5Cfrac%7Bd%7D%7B2%7D)
![L_{lake} = \frac{1269.1}{2}](https://tex.z-dn.net/?f=L_%7Blake%7D%20%3D%20%5Cfrac%7B1269.1%7D%7B2%7D)
![L_{lake} = 634.55m](https://tex.z-dn.net/?f=L_%7Blake%7D%20%3D%20634.55m)
Therefore the length of the lake is 634,55m
According to Stefan-Boltzmann Law, the thermal energy radiated by a radiator per second per unit area is proportional to the fourth power of the absolute temperature. It is given by;
P/A = σ T⁴ j/m²s
Where; P is the power, A is the area in square Meters, T is temperature in kelvin and σ is the Stefan-Boltzmann constant, ( 5.67 × 10^-8 watt/m²K⁴)
Therefore;
Power/square meter = (5.67 × 10^-8) × (3000)⁴
= 4.59 × 10^6 Watts/square meter