For one mole of an ideal gas , which of these statements must be true ?
(i)     U and  H  each depends only on temperature
(ii)    Compressibility factor  z is not equal to 1
(iii)   $C_{p.m}-C_{v.m}=R$
(iv)   $dU=C_{V}dT$ for any process

Internal energy($\mathrm{U}$) of an ideal gas depends only on temperature($\mathrm{T}$), neither on volume($\mathrm{V}$) nor the pressure($\mathrm{P}$)

The heat absorbed by gas is equal to its internal heat engine, when ideal gas undergoes process involving only $\mathrm{P}-\mathrm{V}$work.

Therefore, for an ideal gas,

$$\begin{gathered} {\mathrm{C}}_{\mathrm{v}}=\mathrm{dV}/\mathrm{dT} \\ \mathrm{du}={\mathrm{C}}_{\mathrm{V}}\mathrm{dT} \end{gathered}$$

For an ideal gas, Z=1