`q=-w=nRT1n(v_(f)-v_(i))` is for isothermal ………change.

q=w=-p_(ext)(v_(f)-v_(i)) is for irreversible…. Change.

If the boundary of system moves by an infinitesimal amount, the work involved is given by dw=-P_("ext")dV for irreversible process w=-P_("ext")DeltaV " "( "where "DeltaV=V_(f)-V_(i)) for reversible process P_("ext")=P_("int")pmdP~=P_("int") so for reversible isothermal process w = -nRTln.(V_(f))/(V_(i)) 2mole of an ideal gas undergoes isothermal compression along three different paths : (i) reversible compression from P_(i)=2 bar and V_(i) = 8L to P_(f) = 20 bar (ii) a single stage compression against a constant external pressure of 20 bar, and (iii) a two stage compression consisting initially of compression against a constant external pressure of 10 bar until P_("gas")=P_("ext") , followed by compression against a constant pressure of 20 bar until P_("gas") = P_("ext") Order of magnitude of work is :

If the boundary of system moves by an infinitesimal amount, the work involved is given by dw=-P_("ext")dV for irreversible process w=-P_("ext")DeltaV " "( "where "DeltaV=V_(f)-V_(i)) for reversible process P_("ext")=P_("int")pmdP~=P_("int") so for reversible isothermal process w = -nRTln.(V_(f))/(V_(i)) 2mole of an ideal gas undergoes isothermal compression along three different plaths : (i) reversible compression from P_(i)=2 bar and V_(i) = 8L to P_(f) = 20 bar (ii) a single stage compression against a constant external pressure of 20 bar, and (iii) a two stage compression consisting initially of compression against a constant external pressure of 10 bar until P_("gas")=P_("ext") , followed by compression against a constant pressure of 20 bar until P_("gas") = P_("ext") Order of magnitude of work is :

If the boundary of system moves by an infinitesimal amount, the work involved is given by dw= -P_("ext") dV , for irreversible process W= -P_("ext") Delta V (where Delta V= V_(f) - V_(i) ). For reversible process. P_("ext") = P_("int") +- dP ~= P_("int") , so for reversible isothermal process W = -nRT "In" (V_(f))/(V_(i)) 2 mole of an ideal gas undergoes isothermal compression along three different paths: (i) reversible compression from P_(i) = 2 bar and V_(i) = 8L " to" P_(f) = 20 bar (ii) a single stage compression against a constant external pressure of 20 bar (iii) a two stage compression consisting initially of compression against a constant external pressure of 10 bar until P_("gas") = P_("ext") , followed by compression aganist a constant pressure of 20 bar until P_("gas") = P_("ext") Work done (in bar -L) on the gas in reversible isothermal compression is:

The pressure-volume of varies thermodynamic process is shown in graphs: Work is the mole of transference of energy. It has been observed that reversible work done by the system is the maximum obtainable work. w_(rev) gt w_(irr) The works of isothermal and adiabatic processes are different from each other. w_("isothermal reversible") = 2.303 nRT log_(10) ((V_(2))/(V_(1))) = 2.303 nRT log_(10)((P_(2))/(P_(1))) w_("adiabatic reversible") = C_(V) (T_(1)-T_(2)) A thermodynamic system goes in a cyclic process as represented in the following P -V diagram: The network done during the complete cycle is given by the area