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Yes, the probability for the electron to be found inside the nucleus is, for some atomic orbitals, non-zero. However, you must recall that these orbitals usually assume a point charge for the nucleus, and so they may not be a valid when you "zoom in" to the nucleus. Nevertheless, there's nothing inherently wrong with the electron being where the proton is - ...


3

No. The parcel of gas expands adiabatically as it rises. This makes it cool. Here's one way of looking at what happens: No heat is transferred to or from the parcel of gas (so, adiabatic). At the same time, the parcel of gas expands as it rises. That means the parcel is doing work on the external environment. The temperature of the parcel must drop to ...


2

AdS black holes exist in various dimensions, $p=3$ is not the only choice. The parameter can take on values above or below $3$. One famous example is the three-dimensional BTZ black hole, and higher dimensional ones are also frequently used in the correspondence. Furthermore, I think there is a misunderstanding on the concept of a "gravity dual". The metric ...


2

Since gas molecules are affected by gravity, wouldn't that make gas molecules at higher than average elevation slower (at the top of their ballistic parabola) and thus colder than air molecules accelerating to the ground? In non-relativistic theory no, because in thermodynamic equilibrium temperature has to be the same everywhere. The slowing down does ...


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This is a very old question, but none of the answers fully address the question. I'll frame my answer in terms of answers to a series of questions: How much does temperature vary with altitude? Why does pressure vary with altitude? Why does temperature vary with altitude? What about the second law of thermodynamics? Why is the Tibetan Plateau so cold so ...


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Because what you are doing is a flow process, with mass inflow and no mass outflow, you need to use the thermodynamic equation: $dU_{cv}={m_{in}d}{H}_{in}-{m_{out}d}H_{out}+\delta Q-\delta W_{shaft}$ If you insulate your air cylinder well enough, $\delta Q = 0$. Assuming that your air cylinder does not deform, $\delta W = 0$. Since you are filling your ...


2

First and foremost, a primer over what "buoyancy" is is needed. Pressure decreases with altitude. The atmospheric pressure at the top of the balloon is a tiny bit less than the atmospheric pressure at the bottom of the balloon. This pressure difference results in a tiny net upward force on the balloon. The balloon rises if this tiny net upward force exceeds ...


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I believe the confusion is that you believe pressure will always increase as temperature increases. This is only the case in a closed environment such as inside the tire. In an environment such as the atmosphere which is, essentially, in an unconfined environment, the density will decrease with temperature as well. This does not happen inside of a closed ...


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The lens works because it takes all the sunlight falling on its area, $A_1$, and focuses it onto a small spot $A_2$. The intensity in the spot is the intensity of the sunlight multiplied by $A_1/A_2$. Exactly the same applies to a mirror. So provided your mirror has the same cross sectional area as the lens, and provided it can focus the light as ...


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There are, by my count, 33 other official weather observation stations within Sydney. Here's a map: With regard to the Sydney - Observation Hills (Station ID 066062) station -- That freeway didn't exist when the station was built. How could it? That station dates back to 1858. The station was moved 150 meters to its current location in 1917. That tiny ...



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