WORK DONE (PV-WORK ANALYSIS )

Energy that is transmitted from one system to another in such a way that difference of temperature is not directly involved. This definition is consistent with our understanding of work as dw= Fdx. The force (F) can arise from electrical, magnetic, gravitational & other sources. It is a path function.

PV-Work analysis: Consider a cylinder fitted with a friction less piston, which enclosed no more of an ideal gas. Let an external force F pushes the piston inside producing displacement in piston.

Let distance of piston from a fixed point is x and distance of bottom of piston at the same fixed point is l. This means the volume of cylinder = (l – x) A where A is area of cross section of piston.

For a small displacement dx due to force F, work done on the system.

                        dw = F.dx

                                                  Also  F = PA 

                        dW = PA.dx

                                                    V = (l – x)A

                         dV = –A . dx

                        dW = –Pext. dV

             

Note :

(1): Litre atmosphere term is unit of energy. It is useful to remember the conversion: 

         1 litre atm= 101.3 Joules = 24.206 Cal.

(2): During expansion dV is positive and hence sign of w is negative since work is done by the system and negative sign representing decease in energy content of system. During compression, the sign of dV is negative which gives positive value of w representing the increase in energy content of system during compression.

EXAMPLE.1 mole of ideal monatomic gas at 27°C expands adiabatically against a constant external pressure of 1.5 atm from a volume of 4dm³ to 16 dm³.            Calculate (i) q (ii) w and (iii) DU

SOLUTION:   (i) Since process is adiabatic  \ q = 0

                       (ii) As the gas expands against the constant external pressure.

                             W = - PVd=-P(V2-V1)

                             W =-1.5(16-4)

                             W= - 18 dm³

                            (iii) DU = q + w = 0 + (-18) = -18 atm dm³

(1) Work done in Isothermal Irreversible Process:
(2) Work done in Isothermal Reversible Process:
(3) Work done in Adiabatic Irreversible Process:
(4) Work done in Adiabatic Reversible Process: