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Zeroth Law of Thermodynamics

Which of the ...

Question

Which of the following thermodynamics relation is correct?

d G = V d P - S d T

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d U = P d V + T d S

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d H = - V d p + T d S

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d G = V d P + S d T

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Solution

The correct option is A $d G = V d P - S d T$
$d G = d H - T d S - S d T$ ... $(G = H - T S)$
$d H = d U + P d V + V d P$ ... $(H = U + P V)$
and $d U = T d S - P d V$
$∴$ $d G = (T d S - P d V) + P d V + V d P - T d S - S d T$
$d G = V d P - S d T$

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