Use the Gibbs expression for entropy (eqn 14.48) to derive the formula for the entropy of mixing (eqn 14.40). elow are equations 14.48 and 14.40 AS = −NkB(x ln x + (1 − x) ln(1 − x)). - - (14.40) S=-kB Piln P¿. (14.48)

When 1.60×105 J of heat transfer occurs into a meat pie initially at 21.5 °C, its entropy increases by 483 J/K.. Estimate the final temperature of the pie.

The probability of a system being in the ith mi- crostate is P₁ = e/Z, (14.56) where E is the energy of the ith microstate and ẞ and Z are constants. Show that the entropy is given by S/kB = In Z+BU, where U=PE is the internal energy. (14.57)

A box contains 100 gas molecules all released on the left side of the box. What is the initial entropy of all the gas molecules on one side? You can calculate the number of microstates (left/right distribution of molecules) possible by the equation W = N! / ( nL! * nR!,) where N is the total number of molecules and nL is the number on the left and nR is the number on the right. What is the entropy of the most disorganized distribution of gas molecules?