Is the Work Done on a System Positive When There is Compression?

[eep]

In terms of the thermodynamic identity:

$$dU = {\tau}d{\sigma} - pdV$$

the term for the work done on the system ($-pdV$) must be positive if there is a compression, in which case dV would be negative, correct? If one wanted to write the identity in terms of the work done *by* the system, you would simply switch the sign.

 

[dextercioby]

It can be as easily the other way around (the work done on the system be negative), it only matters that the sign you choose be kept in all calculations, else what you'd be doing wouldn't make any sense.

Daniel.

 

[charng]

Yes, that is correct. The work done on the system would be positive if there is compression, as it would require an external force to compress the system and decrease its volume (dV < 0). This is reflected in the negative sign in front of the pdV term in the thermodynamic identity. If one wanted to write the identity in terms of the work done by the system, the sign of the work term would be switched to positive, as the system would be doing work on its surroundings by expanding (dV > 0).