Explain how calculate entropy in spontaneous mixing of ideal gases at constant temperature and p?
When gases freely mix with each other at constant temperature and pressure, each of the gases can be thought of as undergoing a free expansion from initial volume to the same final volume V_f, where V_f = V_a+V_b + .... ; degree of randomness as well as entropy of gas molecules increase. The change in entropy per mole of the mixtureof ideal gases formed can be calculated by
ΔS_(mix) = – R Ʃx_ilnx_i
Where xi is the mole fraction of the ith species in the mixture. Since xi <1, ΔS_(mix) is positive, i.e. entropy increases during mixing.
This is a unique case where entropy (often defined as dq/T) increases though heat transfer (dq) is zero, and yet the behaviour of spontaneity of the process of mixing could be correctly predicted on the basis of entropy alone.