# Adiabatic closed system work

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.

• pl.check whether your path is reversible or irreversible- in general p.dv will be path dependent. – drvrm Aug 31 '18 at 12:00
• @shashank tyagi. Think we are going around in circles so I am withdrawing my answer. However, if the process is adiabatic then there is only one value of work for that particular process. But that work depends on it being an adiabatic process. I was only trying to prove that there is no unique value of work between the two states that you happen to connect by an adiabatic process. You said it is a closed system, but then there is no mass transfer regardless of the speed of the process. You also said it is adiabatic. Therefore there is no heat transfer regardless of the speed of the process. – Bob D Aug 31 '18 at 18:05
• That is how adiabatic process avoids heat transfer, either by very high speed process or by heavy insulation, so no it won't be adiabatic regardless of speed(only if insulation is mentioned, then it can). I agree with you that there is no unique value of work between two states but I think you misunderstood the question, you said there is only one value of work for that particular adiabatic process, which would also be true for other processes, if you pick one & fix the path to it, like a particular isothermal process(please note a particular not any isothermal process). Continued in next... – shashank tyagi Sep 1 '18 at 3:36
• But I think the question boil downs to the another question that can there be multiple adiabatic processes between given two states, for which the work would be same? Because the derivation in question just mentions the process is adiabatic, it doesn't mention that it is a particular unique adiabatic process. So can there be multiple adiabatic processes between two states? If there can be, then for all of them dQ=0, & according to derivation it appears for all of those different adiabatic paths, work would be same. – shashank tyagi Sep 1 '18 at 3:42
• Maybe you define a closed system adiabatic process different than I am aware of. The definitions I know are: (1) a closed system is defined as one that does not exchange mass with its surroundings and (2) an adiabatic process is one involving no heat transfer between a system and its surroundings, owing to the nature of the boundary between them (normally a perfectly thermally insulated boundary). As far as I know, these apply regardless of the speed of the process. Can you cite a reference that heat/mass transfer for a closed system adiabatic process depends on the speed of the process? – Bob D Sep 1 '18 at 12:24