Helmholtz free energy (A) is defined as:

d A = d E - d (T S)

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d A = d H - d (T S)

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d A = d E + d (T S)

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none of these

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Solution

The correct option is B $d A = d E - d (T S)$
In thermodynamics, the Helmholtz free energy is a thermodynamic potential that measures the “useful” work obtainable from a closed thermodynamic system at a constant temperature and volume.
$d A = d E - d (T S)$

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