An ideal gas at absolute temperature t is in a uniform gravitational field with acceleration due to gravity g in the negative z-direction. (a) by considering the gravitational potential energy of a molecule, derive an expression for the density of molecules n(z) as a function of height z. (b) how does your expression for n(z) compare with that obtained by writing the condition of hydrostatic equilibrium for a slice of the gas located between heights z and z + dz?

Alinearly polarized electromagnetic wave has an average intensity of 196 w/m^2. this wave is directed towards two ideal polarizers (in real polarizers, transmission is also effected by reflection and absorption). polarizer a is oriented with its transmission axis at an angle of θ_1=20.8∘ with the incident electric field. polarizer b has its axis at an angle of θ_2=63.0∘ with the incident electric field. what is the average intensity of the wave after it passes through polarizer a? what is the average intensity of the wave after it passes through polarizer b? suppose that the two polarizers a and b are interchanged. what would the average intensity be after passing through both polarizers?

Ascientist notices that an oil slick floating on water when viewed from above has many different colors reflecting off the surface, making it look rainbow-like (an effect known as iridescence). she aims a spectrometer at a particular spot and measures the wavelength to be 750 nm (in air). the index of refraction of water is 1.3

Aloop of wire is in a magnetic field such that its axis is parallel with the field direction. which of the following would result in an induced emf in the loop? choose all that apply. a loop of wire is in a magnetic field such that its axis is parallel with the field direction. which of the following would result in an induced emf in the loop? choose all that apply. moving the loop outside of the magnetic field region. spin the loop such that its axis does not consistently line up with the magnetic field direction. change the magnitude of the magnetic field. change the diameter of the loop