Amagnetic field b such that the energy of 2. consider a spin ½ magnet with n spins in the spin up state e↑ ε heat bath at temperature t whereas e. +ε . suppose the magnet is in contact with a (a) calculate the internal energy, entropy and free energy as a function of x -n/n where n = n-n, . you may assume n, and n, are both large numbers so you can apply stirling's approximation. hint: keep only the first two terms in stirling's approximation but do not assume x < < 1 . (b) what value of x minimizes the free energy and call it x? (c) make a plot of x. q versus t and explain the low temperature and high temperature limits.

Asubject in a clinical research trial experiences a serious, unanticipated adverse drug experience. how should the investigator proceed, with respect to the irb, after the discovery of the adverse event occurrence? a. do not report the adverse drug experience to the irb since it is a common adverse experience.b. report the adverse drug experience to the irb only if there are several other occurrences.c. report the adverse drug experience as part of the continuing review report.d. report the adverse drug experience in a timely manner, in keeping with the irb's policies and procedures, using the forms or the mechanism provided by the irb.

Aspring has a natural length of 8 m. if a 12-n force is required to keep it stretched to a length of 10 m, how much work w is required to stretch it from 8 m to 16 m? (round your answer to two decimal places.)

Astudent pushes a 60-n block across the floor for a distance of 10 m. how much work was done to move the block