We all know that climbing a mountain top via a very steep path is more strenuous than reaching the same mountain top by a long winding path. This is an illustration of a general feature that work depends on the path followed in a process. The same is true for the heat exchanged between the system and the surroundings. Consider a gas enclosed in a cylinder as shown in Fig 21.1
Fig 21.1 Gas enclosed in a cylinder. Initial volume V1, and pressure P1.
The initial volume is V1 and the pressure is P1 . When the gas is allowed to expand infinitesimally slowly from P1 to P2, the gas may be considered to be at equilibrium throughout and the work done is given by
wr = F.dx = (F/A) (Adx) = PdV
(21.1)
Here, F is the force on the piston, dx is the increment in the distance moved by the piston and A is the area of the piston. This is the work done by the gas on the surroundings and is positive during an expansion.The work done on the gas, or the work added to the gas is
