Which is the correct statement ?

According to ideal gas equation for one mole of gas, PV = RT

For isothermal process, T = constant;

$\Rightarrow \mathrm{P}V=\text{ Constant. }$

For isothermal process, change in internal enerqy is zero, as

$\mathrm{U}={\mathrm{nC}}_{\mathrm{V}}\mathrm{\Delta T}$

For adiabatic change,

$P{V}^{\gamma }=\text{ Constant }$

$\Rightarrow \frac{P_2}{P_1}={\left(\frac{V_1}{V_2}\right)}^{\gamma }$

In adiabatic process, heat given or taken out of system is zero.