NATURE OF HEAT AND WORK:-

                                         NATURE OF HEAT AND WORK:-                            

Work: - Work is the one of the means by which system can exchange energy with its surroundings.

                                 Work = force X displacement

                                                   W = f X d              

                                            

Expression for pressure volume type work (Pressure constant):-                             

                   Consider a certain amount of ideal gas at pressure P, Volume V₁ and temp. T   enclosed in a cylinder fitted with weight less, friction less movable piston

                           As the gas expands; it pushes the piston up word through a distance d,   against external opposing force F.                                                                                              

            W = Opposing force X distance                                                               

             W = -F X d    (- ve sign indicated the lowering of energy                                      of the system)       
            

          Force = pressure X area                                                                                                                                                                                    
                F =   P_ext X A

          W = - P_ext X A X d     

But area x distance = change in volume (A X d = ∆V)

             W = - P_ext X ∆V               OR                          

             W = - P_ext X (V₂ – V₁)

This is expression for expansion of gas. if compression is takes placed then                    
                W = + Pext X (V₂ – V₁)

Expression for Maximum work done during isothermal reversible expansion of an Ideal gas                  

                                                                                                                                                                                           Consider n mole of an ideal gas enclosed in cylinder fitted with weight less friction less movable piston.

                                  Let external pressure and internal pressure of the gas is same at constant temperature external pressure is decrease by very small volume  say dp then their small change in volume say dv and hence work done takes placed in small amount  dw

                       

                         Work = External pressure X Change in volume

                             dw = -P_ext X dv                        (P- P_ext = dp) 

                             dw = - ( P-dp) X dv               

         dw = - Pdv + dpdv       

Since dpdv is very small hence it is neglected                                                                  

      dw = - Pdv                                                                          

for an ideal gas      PV  =  nRT                                                                                         

                                   P  =  nRT / V                                                                                               

                                 dw  =  - nRT   dv/v --------------     1         

 Integrated equation. 1 between initial volume V₁ and final volume V₂           

                         

                          

                                   W =  - nRT [log_e V₂ – log_e V₁ ]

                                    W =   -  nRT log_e V₂ /V₁

                                     W =    - 2.303 nRT log₁₀ V₂ /V₁ 

But the process is reversible hence maximum work done is take place W =Wmax

                                 

                                      W_max = - 2.303 nRT log₁₀ V₂ /V₁

     

 Acc^rd. To Boyles law   P₁V₁    =  P₂V₂     

                                             V₂/ V₁ = P₁/ P₂

                                      W_max = - 2.303 nRT log₁₀ P₁/ P₂

For one mole of an ideal gas the above equation is written as follow

                                 

                                   W_max = - 2.303 RT log₁₀ P₁/ P₂                        when n = 1

                             

                                    W_max = - 2.303 RT log₁₀ V₂ /V₁                       when n = 1

This is equation (expression) for work done during isothermal reversible expansion of an ideal gas

         Where,  W_max = maximum work done in joules

                          n = Number of moles

                          R = gas constant = 8.314Jk^-1mole ^-1  

                           T = Temperature. in Kelvin ( K)

                           V₁ and V₂ = Initial and final volume in m³ or dm³ respectively

                            P₁ and P₂ = Initial and final pressure in Pascal (Nm^-2 ) respectively