Answer:
Because the Earth has so much gravity, it can hold water, land, and life in it's atmosphere.
(Not sure what beaker you are talking about, so sorry) But I don't think the moon's gravity would have an effect on a beaker of water because the Earth's gravity is much more than the moon's.
I think you would be able to feel a little bit of Earth's gravity on the moon because the Earth's gravity pulled the moon into orbit, therefore, gravity on Earth my have some effect on the moon.
hope this helps!
To solve the problem it is necessary to apply the concepts related to the conservation of energy through the heat transferred and the work done, as well as through the calculation of entropy due to heat and temperatra.
By definition we know that the change in entropy is given by
![\Delta S = \frac{Q}{T}](https://tex.z-dn.net/?f=%5CDelta%20S%20%3D%20%5Cfrac%7BQ%7D%7BT%7D)
Where,
Q = Heat transfer
T = Temperature
On the other hand we know that by conserving energy the work done in a system is equal to the change in heat transferred, that is
![W = Q_{source}-Q_{sink}](https://tex.z-dn.net/?f=W%20%3D%20Q_%7Bsource%7D-Q_%7Bsink%7D)
According to the data given we have to,
![Q_{source} = 200000Btu](https://tex.z-dn.net/?f=Q_%7Bsource%7D%20%3D%20200000Btu)
![T_{source} = 1500R](https://tex.z-dn.net/?f=T_%7Bsource%7D%20%3D%201500R)
![Q_{sink} = 100000Btu](https://tex.z-dn.net/?f=Q_%7Bsink%7D%20%3D%20100000Btu)
![T_{sink} = 600R](https://tex.z-dn.net/?f=T_%7Bsink%7D%20%3D%20600R)
PART A) The total change in entropy, would be given by the changes that exist in the source and sink, that is
![\Delta S_{sink} = \frac{Q_{sink}}{T_{sink}}](https://tex.z-dn.net/?f=%5CDelta%20S_%7Bsink%7D%20%3D%20%5Cfrac%7BQ_%7Bsink%7D%7D%7BT_%7Bsink%7D%7D)
![\Delta S_{sink} = \frac{100000}{600}](https://tex.z-dn.net/?f=%5CDelta%20S_%7Bsink%7D%20%3D%20%5Cfrac%7B100000%7D%7B600%7D)
![\Delta S_{sink} = 166.67Btu/R](https://tex.z-dn.net/?f=%5CDelta%20S_%7Bsink%7D%20%3D%20166.67Btu%2FR)
On the other hand,
![\Delta S_{source} = \frac{Q_{source}}{T_{source}}](https://tex.z-dn.net/?f=%5CDelta%20S_%7Bsource%7D%20%3D%20%5Cfrac%7BQ_%7Bsource%7D%7D%7BT_%7Bsource%7D%7D)
![\Delta S_{source} = \frac{-200000}{1500}](https://tex.z-dn.net/?f=%5CDelta%20S_%7Bsource%7D%20%3D%20%5Cfrac%7B-200000%7D%7B1500%7D)
![\Delta S_{source} = -133.33Btu/R](https://tex.z-dn.net/?f=%5CDelta%20S_%7Bsource%7D%20%3D%20-133.33Btu%2FR)
The total change of entropy would be,
![S = \Delta S_{source}+\Delta S_{sink}](https://tex.z-dn.net/?f=S%20%3D%20%5CDelta%20S_%7Bsource%7D%2B%5CDelta%20S_%7Bsink%7D)
![S = -133.33+166.67](https://tex.z-dn.net/?f=S%20%3D%20-133.33%2B166.67)
![S = 33.34Btu/R](https://tex.z-dn.net/?f=S%20%3D%2033.34Btu%2FR)
Since
the heat engine is not reversible.
PART B)
Work done by heat engine is given by
![W=Q_{source}-Q_{sink}](https://tex.z-dn.net/?f=W%3DQ_%7Bsource%7D-Q_%7Bsink%7D)
![W = 200000-100000](https://tex.z-dn.net/?f=W%20%3D%20200000-100000)
![W = 100000 Btu](https://tex.z-dn.net/?f=W%20%3D%20100000%20Btu)
Therefore the work in the system is 100000Btu
Density can be kg/m^3 or g/cm3
In g/cm3 density =mass /volume =111g/23cm3
=4.826g/cm3.
In kg/m3,density=mass/volume. converting mass in grams to kg, 1000g=1kg,111g=0.111kg.
cm3 to m3, 1cm3=10^-6m3, 23cm3=0.000023m3
density=0.111kg/0.000023m3 or 2.3*10^-5=4,826.1kg/m3.
the other is a long process.
Answer:
The beam of light is moving at the peed of:
km/min
Given:
Distance from the isalnd, d = 3 km
No. of revolutions per minute, n = 4
Solution:
Angular velocity,
(1)
Now, in the right angle in the given fig.:
![tan\theta' = \frac{y}{3}](https://tex.z-dn.net/?f=tan%5Ctheta%27%20%3D%20%5Cfrac%7By%7D%7B3%7D)
Now, differentiating both the sides w.r.t t:
![\frac{dtan\theta'}{dt} = \frac{dy}{3dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdtan%5Ctheta%27%7D%7Bdt%7D%20%3D%20%5Cfrac%7Bdy%7D%7B3dt%7D)
Applying chain rule:
![\frac{dtan\theta'}{d\theta'}.\frac{d\theta'}{dt} = \frac{dy}{3dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdtan%5Ctheta%27%7D%7Bd%5Ctheta%27%7D.%5Cfrac%7Bd%5Ctheta%27%7D%7Bdt%7D%20%3D%20%5Cfrac%7Bdy%7D%7B3dt%7D)
![sec^{2}\theta'\frac{d\theta'}{dt} = \frac{dy}{3dt} = (1 + tan^{2}\theta')\frac{d\theta'}{dt}](https://tex.z-dn.net/?f=sec%5E%7B2%7D%5Ctheta%27%5Cfrac%7Bd%5Ctheta%27%7D%7Bdt%7D%20%3D%20%5Cfrac%7Bdy%7D%7B3dt%7D%20%3D%20%281%20%2B%20tan%5E%7B2%7D%5Ctheta%27%29%5Cfrac%7Bd%5Ctheta%27%7D%7Bdt%7D)
Now, using
and y = 1 in the above eqn, we get:
![(1 + (\frac{1}{3})^{2})\frac{d\theta'}{dt} = \frac{dy}{3dt}](https://tex.z-dn.net/?f=%281%20%2B%20%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B2%7D%29%5Cfrac%7Bd%5Ctheta%27%7D%7Bdt%7D%20%3D%20%5Cfrac%7Bdy%7D%7B3dt%7D)
Also, using eqn (1),
![8\pi\frac{10}{9})\theta' = \frac{dy}{3dt}](https://tex.z-dn.net/?f=8%5Cpi%5Cfrac%7B10%7D%7B9%7D%29%5Ctheta%27%20%3D%20%5Cfrac%7Bdy%7D%7B3dt%7D)
![\frac{dy}{dt} = \frac{80\pi}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20%5Cfrac%7B80%5Cpi%7D%7B3%7D)