A gaseous system undergoes a change in temperature and volume. What is the entropy change for a particle in this system if the final number

Question

A gaseous system undergoes a change in temperature and volume. What is the entropy change for a particle in this system if the final number of microstates is 0.559 times that of the initial number of microstates?

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Edana Edana 5 years 2021-08-29T04:56:16+00:00 1 Answers 131 views 0

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  1. thienan
    0
    2021-08-29T04:58:12+00:00
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    Explanation:

    According to Boltzmann formula of entropy,

                          S = K ln(W)

    where,     S = Entropy

            K = Boltzmann constant = 1.381 \times 10^{-23} JK^{-1}

             W = Number micro-states

    This equation is valid if total energy is constant and we are assuming here that the total energy is constant over here.

    Let initial W_{i} = 1 then final W_{f} = 0.487

    Now,   \Delta S = K (ln W_{f} - ln W_{i})

                             = 1.381 \times 10^{-23} (ln(0.487) - ln(1) )

                             = 1.381 \times 10^{-23} \times (-0.71949)

                             = -9.936 \times 10^{-24} JK^{-1}

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