Question
Show that a spontaneous chemical process that is carried out in a closed system at constant S and P is driven by a decrease in enthalpy.

Please help. Thank you!


how that a spontaneous chemical process that is carried out in a closed system at con- stant S and P is driven by a decrease in enthalpy. Hint: Start with the fundamental equation for dH and note that Σ μǐdNF SVVNs then use the rectified form of the Clausius inequality.

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Answer #1

dH=TdS+VdP+∑μidn

Now as we see that we are already givena state where S and P are constant

so dP and dS are zero

dH = ∑μidn = dWn

The claussius inequality states that dQ/T <0

so from this and the above derived equation we can see that the system is surely derived by a decrease in enthalpy as we get a negative value of enthalpy

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