Question

The temperature of a sample of carbon dioxide gas was altered without altering the volume of the system.

(a) Calculate the entropy change for the system if the final number of microstates is 0.713 times the initial number of microstates in the system.

J/K:

(b) Determine whether the temperature of the gas was raised or lowered, and explain your answer.

Because the number of microstates (increased, remianed unchanged, or decreased) and the entropy (increased, remianed unchanged, or decreased), we can predict that the temperature of the gas was (raised or lowered).

Answer 1

ΔS = k ln(W_final / W_initial )

where, ΔS = entropy change,

k = Boltzmann constant = 1.38 x 10^-23 J/K

W_final = final number of microstates

W_initial = initial numberof microstates

=> ΔS = 1.38 x 10^-23 J/K x ln( 0.713/1)

=> ΔS = -4.67 x 10^-24 J/K

(b) the temperature of the gas was lowered, since , entropy change is negative that means entropy is decreased. Usually entropy increases with increase in temperature. And more over number of microstates are aslo decreased here, so that we can say that the temperature of the gas was lowered,