Answer:
a. 9947 m
b. 99476 times
c. 2*10^11 molecules
Explanation:
a) To find the mean free path of the air molecules you use the following formula:
![\lambda=\frac{RT}{\sqrt{2}\pi d^2N_AP}](https://tex.z-dn.net/?f=%5Clambda%3D%5Cfrac%7BRT%7D%7B%5Csqrt%7B2%7D%5Cpi%20d%5E2N_AP%7D)
R: ideal gas constant = 8.3144 Pam^3/mol K
P: pressure = 1.5*10^{-6} Pa
T: temperature = 300K
N_A: Avogadros' constant = 2.022*10^{23}molecules/mol
d: diameter of the particle = 0.25nm=0.25*10^-9m
By replacing all these values you obtain:
![\lambda=\frac{(8.3144 Pa m^3/mol K)(300K)}{\sqrt{2}\pi (0.25*10^{-9}m)^2(6.02*10^{23})(1.5*10^{-6}Pa)}=9947.62m](https://tex.z-dn.net/?f=%5Clambda%3D%5Cfrac%7B%288.3144%20Pa%20m%5E3%2Fmol%20K%29%28300K%29%7D%7B%5Csqrt%7B2%7D%5Cpi%20%280.25%2A10%5E%7B-9%7Dm%29%5E2%286.02%2A10%5E%7B23%7D%29%281.5%2A10%5E%7B-6%7DPa%29%7D%3D9947.62m)
b) If we assume that the molecule, at the average, is at the center of the chamber, the times the molecule will collide is:
![n_{collision}=\frac{9947.62m}{0.05m}\approx198952\ times](https://tex.z-dn.net/?f=n_%7Bcollision%7D%3D%5Cfrac%7B9947.62m%7D%7B0.05m%7D%5Capprox198952%5C%20%20times)
c) By using the equation of the ideal gases you obtain:
![PV=NRT\\\\N=\frac{PV}{RT}=\frac{(1.5*10^{-6}Pa)(\frac{4}{3}\pi(0.05m)^3)}{(8.3144Pa\ m^3/mol\ K)(300K)}=3.14*10^{-13}mol\\\\n=(3.14*10^{-13})(6.02*10^{23})\ molecules\approx2*10^{11}\ molecules](https://tex.z-dn.net/?f=PV%3DNRT%5C%5C%5C%5CN%3D%5Cfrac%7BPV%7D%7BRT%7D%3D%5Cfrac%7B%281.5%2A10%5E%7B-6%7DPa%29%28%5Cfrac%7B4%7D%7B3%7D%5Cpi%280.05m%29%5E3%29%7D%7B%288.3144Pa%5C%20m%5E3%2Fmol%5C%20K%29%28300K%29%7D%3D3.14%2A10%5E%7B-13%7Dmol%5C%5C%5C%5Cn%3D%283.14%2A10%5E%7B-13%7D%29%286.02%2A10%5E%7B23%7D%29%5C%20molecules%5Capprox2%2A10%5E%7B11%7D%5C%20molecules)
Answer:
The pressure difference across hatch of the submarine is 3217.68 kpa.
Explanation:
Gauge pressure is the pressure above the atmospheric pressure. If we consider gauge pressure for finding pressure differential then no need to consider atmospheric pressure as they will cancel out. According to hydrostatic law, pressure varies in the z direction only.
Given:
Height of the hatch is 320 m
Surface gravity of the sea water is 1.025.
Density of water 1000 kg/m³.
Calculation:
Step1
Density of sea water is calculated as follows:
![S.G=\frac{\rho_{sw}}{\rho_{w}}](https://tex.z-dn.net/?f=S.G%3D%5Cfrac%7B%5Crho_%7Bsw%7D%7D%7B%5Crho_%7Bw%7D%7D)
Here, density of sea water is
, surface gravity is S.G and density of water is
.
Substitute all the values in the above equation as follows:
![S.G=\frac{\rho_{sw}}{\rho_{w}}](https://tex.z-dn.net/?f=S.G%3D%5Cfrac%7B%5Crho_%7Bsw%7D%7D%7B%5Crho_%7Bw%7D%7D)
![1.025=\frac{\rho_{sw}}{1000}](https://tex.z-dn.net/?f=1.025%3D%5Cfrac%7B%5Crho_%7Bsw%7D%7D%7B1000%7D)
kg/m³.
Step2
Difference in pressure is calculated as follows:
![\bigtriangleup p=rho_{sw}gh](https://tex.z-dn.net/?f=%5Cbigtriangleup%20p%3Drho_%7Bsw%7Dgh)
![\bigtriangleup p=1025\times9.81\times320](https://tex.z-dn.net/?f=%5Cbigtriangleup%20p%3D1025%5Ctimes9.81%5Ctimes320)
pa.
Or
![\bigtriangleup p=(3217680pa)(\frac{1kpa}{100pa})](https://tex.z-dn.net/?f=%5Cbigtriangleup%20p%3D%283217680pa%29%28%5Cfrac%7B1kpa%7D%7B100pa%7D%29)
kpa.
Thus, the pressure difference across hatch of the submarine is 3217.68 kpa.
Answer:
13.95
Explanation:
Given :
Vector A polar coordinates = ( 7, 70° )
Vector B polar coordinates = ( 4, 130° )
To find A . B we will
A ( r , ∅ ) = ( 7, 70 )
A = rcos∅ + rsin∅
therefore ; A = 2.394i + 6.57j
B ( r , ∅ ) = ( 4, 130° )
B = rcos∅ + rsin∅
therefore ; B = -2.57i + 3.06j
Hence ; A .B
( 2.394 i + 6.57j ) . ( -2.57 + 3.06j ) = 13.95
Answer:
M = 281.25 lb*ft
Explanation:
Given
W<em>man</em> = 150 lb
Weight per linear foot of the boat: q = 3 lb/ft
L = 15.00 m
M<em>max</em> = ?
Initially, we have to calculate the Buoyant Force per linear foot (due to the water exerts a uniform distributed load upward on the bottom of the boat):
∑ Fy = 0 (+↑) ⇒ q'*L - W - q*L = 0
⇒ q' = (W + q*L) / L
⇒ q' = (150 lb + 3 lb/ft*15 ft) / 15 ft
⇒ q' = 13 lb/ft (+↑)
The free body diagram of the boat is shown in the pic.
Then, we apply the following equation
q(x) = (13 - 3) = 10 (+↑)
V(x) = ∫q(x) dx = ∫10 dx = 10x (0 ≤ x ≤ 7.5)
M(x) = ∫10x dx = 5x² (0 ≤ x ≤ 7.5)
The maximum internal bending moment occurs when x = 7.5 ft
then
M(7.5) = 5(7.5)² = 281.25 lb*ft