The closed system work PdV is path dependent but it is path independent for an adiabatic process as can be shown by applying conservation of energy on a closed system (dQ = dE + PdV),here dE is change in energy of system & dQ is change in heat, here for adiabatic dQ=0 , so PdV= -dE, since energy of a system is it's property so it is path independent and hence in this case work is also independent of path).
I have this homework question:
It is desired to bring about a certain change in the state of a system by performing work on the system under adiabatic conditions.
a) The amount of work needed is path dependent.
b) Work alone cannot bring about such a change of state.
c) The amount of work needed is independent of path.
d) More information is needed to conclude anything about the path dependence or otherwise of the work needed.
The answer given is (a). Shouldn't it be (c)? Or is there an exception to above said condition.