How many of the following are correct 

$\text{ i) }{\left(\frac{dH}{dT}\right)}_p-{\left(\frac{dv}{dT}\right)}_v=R\text{ for gas }$

$\text{ ii) }{\left(\frac{\partial H}{\partial T}\right)}_p>{\left(\frac{\partial V}{\partial T}\right)}_v\text{ for liquid }$

$\text{ iii) }{\left(\frac{\partial U}{\partial V}\right)}_T\text{ is zero for ideal gas }$

$\text{ iv) }{\left(\frac{\partial H}{\partial T}\right)}_p>{\left(\frac{\partial U}{\partial T}\right)}_v\text{ for gas }$

v) Heat is a state function

vi) In isothermal process heat is equal to work

vii) Glassy solids at zero Kelvin has entropy equal to zero.

viii) Ideal gas under going expansion in vaccum then the work is maximum.

$\begin{array}{l}\text{ i) }{\left(\frac{\partial H}{\partial T}\right)}_p=C_p;{\left(\frac{\partial U}{\partial T}\right)}_V=C_v\\ C_p-C_v=R\text{ for gas is true }\end{array}$

ii)  $C_p>C_v$for liquid is false because $C_p>C_v$ for gas only 

iii) Internal energy is only a function of temperature for an ideal gas.

$\therefore$change in internal energy at constant temperature is zero

${\left(\frac{\partial U}{\partial V}\right)}_T=0\text{ is true }$

iv)  $C_p>C_v$ for gases is true

v) Heat is a path function so given statements false

vi) According to law   $\Delta U=Q+W$

In isothermal process $\Delta U=0$

Q = W

$\therefore$Heat change = work  in iso thermal process is true

VII) According to third law of thermodynamics entropy of pure and perfect crystalline solid is zero at zero Kelvin but Glass is amorphous solid so given  statement is wrong.

viii) Work done in vaccum is zero 

$\because W=-P_{ex}\Delta V$

In vaccum $P_{ext}=0$

So given statement is false