If heat energy is added to a thermodynamic system, one part increases the internal energy and the other part performs some work.
If heat is added to a system, the system can do work without changing its internal energy. Hence, statement 1 is false.
The formula to calculate the work done is given by
W=∫PdV
From the above equation, it can be concluded that if W>0, i.e., work is done by the system, its volume must increase. Hence, statement II is true.