Let k be the Boltzmann constant.If the thermodynamic state of gas at temperature T changes isothermally and reversibly to a state with three times the number of microstates as initially, the energy input to gas as heat is:
A)Q = 0
B)Q = 3kT
C)Q = -3kT
D)Q = kT ln 3
E)Q = -kT ln 3

Question

Quizplus · Accepted Answer

According to the Boltzmann entropy formula, S = k ln Ω, where Ω is the number of microstates corresponding to a particular macrostate. If the number of microstates triples, then the entropy increases by a factor of ln 3. Since the process is reversible and isothermal, the change in entropy is equal to the heat input divided by the temperature, ΔS = Q/T. Therefore, Q = ΔS × T = kT ln 3.

Let K Be the Boltzmann Constant