Question

my notes ask your teacher there are 73 small disks with one side blue and the other white in a box. when you start there are 52 blue sides up (and 21 white sides up). after you shake the box, you find that there are 35 blue sides up and 38 white sides up. what is the change in entropy? for kb use kb

Answer 1

The change in entropy of the system, represented by the blue sides of the disks, is approximately 3.28 J/K.

To calculate the change in entropy, we can use the formula:

ΔS = -R ln(Pf/Pi)

Where ΔS is the change in entropy, R is the ideal gas constant (8.314 J/(mol·K)), Pf is the final probability, and Pi is the initial probability.

In this case, we can consider the blue sides of the disks as the system. The initial probability of a blue side being up is 52/73, and the final probability is 35/73.

Using these values in the formula, we can calculate the change in entropy:

ΔS = -8.314 J/(mol·K) ln(35/73 / 52/73)

Simplifying the expression:

ΔS = -8.314 J/(mol·K) ln(35/52)

Calculating ln(35/52) ≈ -0.395:

ΔS ≈ -8.314 J/(mol·K) (-0.395)

ΔS ≈ 3.28 J/K