Suppose that when a system is placed in thermal contact with a heat reservoir, which is at absolute temperature tr, it absorbs from the reservoir an amount of heat q. show that the increase in entropy of the system ∆s in this process obeys the inequality ∆s ≥ q/tr, the equals sign applying only if the system’s initial temperature differs infinitesimally from tr.

The image shows a pendulum in simple harmonic motion the pendulum starts at a and swing to e

Suppose that a mass of 2 kg is attached a spring whose spring constant is 50. the system is damped such that b = 12 . the mass is set in motion with an initial velocity of -8 m/s at a position 0 meters from equilibrium. set up and solve a differential equation that models this motion. write your solution in the form a cos ( ω t − α ) where α is a positive number. use your solution to fill in the information below: what is the amplitude of the motion? what is the value of ω ? what is the phase shift?

A10-kg piece of aluminum sits at the bottom of a lake, right next to a 10-kg piece of lead, which is much denser than aluminum. which one has the greater buoyant force on it? explain. b - the aluminum a) both have the same buoyant force. b) the aluminum c) the lead d) it cannot be determined without knowing their volumes.