No heat is absorbed by the system from the surroundings, but work (W) is done on the system.Identify the correct statement from the given following?

The system has adiabatic wall and $∆\mathrm{E}={\mathrm{W}}_{\mathrm{adi}}$

The system has thermally conducting walls and $∆\mathrm{E}\ne -\mathrm{q}$

The system has adiabatic wall and $∆\mathrm{E}\not\equiv {\mathrm{W}}_{\mathrm{adi}}$

The system has thermally conducting walls and $∆\mathrm{E}=-\mathrm{q}$