A. Pressure varies inversely with volume of an ideal gas.

For an isothermal process,

So

$$P\propto\frac{1}{V}$$

A → III

B. Heat absorbed goes partly to increase internal energy and partly to do work.

That is true for isobaric process:

Both $$ΔU$$ and W are generally nonzero.

B → IV

C. Heat is neither absorbed nor released.

That is adiabatic process:

Q=0

C → I

D. No work is done on or by gas.

In isochoric process volume is constant:

$$W=P\Delta V=0$$

D → II