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1. ### Work in adiabatic process

Homework Statement My textbook says that W = i/2Δ(pV) for an adiabatic process. I don't understand :S Homework Equations W=∫pdV The Attempt at a Solution
2. ### Ultrarelativistic approximation

I read that when v≈c, sqrt(1-β2) = sqrt(2*(1-β)). How do you show this mathematically? I have no idea. Thanks! :)
3. ### Circle and Ellipse

What does it mean when one says that "A circle and an ellipse with a focus at the circle’s center can touch each other only at the longer axis"? Can't you, by varying the size of the circle, make it intersect the ellipse in a variety of ways? Thanks! :)
4. ### Phase of Wave

The phase of a wave at (x,t) is a0cosϕ = ℜa0eiϕ. Where did this come from? I know that the phase of a wave is given by ϕ = kx−ωt+ϕ0 but then I am stuck. Please help! Thanks :D
5. ### Simple buoyancy problem

Homework Statement An object suspended in water is lifted out of the water. How does the absolute pressure at the bottom of the water change? Homework Equations The Attempt at a Solution Wouldn't the absolute pressure not change if the object is still directly over the water...
6. ### Electron in box considering effects of gravity

An electron is enclosed in a large rectangular box. Considering gravity, estimate the order of magnitude of the thickness of the layer that is occupied by the electron at the bottom of the box. I thought about this for a long time and I really have no idea how to proceed. Any thoughts?