Which one of the following equations does not correctly represent the law of thermodynamics for the given processes involving an ideal gas ? 
(Assume non-expansion work is zero)

For 1st law of thermodynamics 

$\begin{array}{l}\mathrm{\Delta U}=\mathrm{q}+\mathrm{w}\\ \Rightarrow \text{ For adiabatic process: }\mathrm{q}=0\\ \Rightarrow \mathrm{\Delta U}=\mathrm{w}\left[\text{ From }\right(\mathrm{i}\left)\right]\\ \Rightarrow \text{ For isothermal process }\mathrm{\Delta T}=0\\ \text{ For }{1}^{\text{st }}\mathrm{law},\mathrm{\Delta U}={\mathrm{nC}}_{\mathrm{V}}\mathrm{\Delta T}\\ \therefore \mathrm{q}=-\mathrm{w}\left[\text{ From }\right(\mathrm{i}\left)\right]\end{array}$

For cyclic process : $\mathrm{\Delta U}=0$ [as U is a state function]

$\therefore q=-w$  [from (i)]

For isothermal process : volume is constant

$\begin{array}{l}\mathrm{w}=-\int {\mathrm{P}}_{\mathrm{exI}}\mathrm{dV}\\ \sin \mathrm{cedV}=0\Rightarrow \mathrm{w}=0\\ \Rightarrow \mathrm{U}=\mathrm{q}\left[\text{ From }\right(\mathrm{i}\left)\right]\end{array}$