Given: $d E = T d S - p d V$ and $H = E + p V$ .

Which one of the following relation is true?

d H = T d S + V d p

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d H = S d T + V d p

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d H = - S d T - V d p

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d H = d E - p d V

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Solution

The correct option is A $d H = T d S + V d p$
Given,

$d E = T d S - p d V$ ...(i)

$H = E + p V$ ...(ii)

Differentiating Eq. (ii),we gte:

$d H = d E + p d V + V d p$ ...(iii)

From Eq. (i) and (iii), we get-

$d H = T d s + V d p$

Hence, option A is correct.

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