In thermodynamics, the energy u(s, v) is a function of the entropy, s and volume, v. show that the expressions for pressure (p=-uv) and temperature (t=us) are dictated by the chain rule along with the first law of thermodynamics: du=tds-pdv. now consider the specific case of an ideal monatomic gas with u(s, v)=3/2 nk [ (n/v) exp[s/nk]]2/3 where n is the number of atoms and k is boltzmann’s constant. show that this expression for the energy gives the usual equation of state pv=nkt.

Aprojectile is launched from ground level with an initial velocity of v 0 feet per second. neglecting air resistance, its height in feet t seconds after launch is given by s equals negative 16 t squared plus v 0 t. find the time(s) that the projectile will (a) reach a height of 192 ft and (b) return to the ground when v 0equals112 feet per second. (a) find the time(s) that the projectile will reach a height of 192 ft when v 0equals112 feet per second. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

In science and physics what is the standard unit of measure for speed?

Consider an ideal gas at 27.0 degrees celsius and 1.00 atmosphere pressure. imagine the molecules to be uniformly spaced, with each molecule at the center of a small cube. what is the length l of an edge of each small cube if adjacent cubes touch but don't overlap?