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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

Respuesta :

onyebuchinnaji

Answer:

d. kT ln 3

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)

[tex]Q= kT*\frac{ln \phi _f}{ln \phi_i} \\\\Q= kT*\frac{3ln \phi _i}{ln \phi_i}\\\\Q= kT ln3[/tex]

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

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