# Which one of the following equation is true? (Given, $\delta E = T\delta S -P\delta V$ and $H=E+PV$)

(a) $\delta H = T\delta S + V\delta P$
(b) $\delta H = S\delta T + V\delta P$
(c) $\delta H = -S\delta T + V\delta P$
(d) $\delta H = \delta E + P\delta V$

Answer: $\delta H = T\delta S + V\delta P$
Given, $H = E + PV$
Differentiating both sides we get,
$\delta H = \delta E + P\delta V + V \delta P$
$\Rightarrow \delta H = T\delta S - P \delta V + P\delta V + V\delta P$
$\therefore \delta H = T\delta S + V \delta P$ $[\because \delta E = T\delta S - P\delta V]$