Question

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. kT ln 3
e. −kT ln 3

Answer 1

d. kT ln 3

Step-by-step explanation:

Given;

k as Boltzmann constant

Let initial initial microstate, = Фi

Let the final microstate, = Фf = 3Фi

at constant temperature, T

The energy input to gas as heat is given by;

Q = TΔS = Tk(lnФf - lnФi)

`Q= kT*(ln \phi _f)/(ln \phi_i) \\\\Q= kT*(3ln \phi _i)/(ln \phi_i)\\\\Q= kT ln3`

Therefore, the energy input to gas as heat is kT ln 3