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q=-w=nRT1n(v(f)-v(i)) is for isothermal ...

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

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`q=-w ="nRT in " V_(f)/V_(l)` is for isothermal reversible change
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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") 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:

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") Order of magnitude work is

If the boundary of system moves by an infinitiesimal amount, the work involved is given by dw= -P_("ext") dV, for irreversible process W= -P_("ext") Delta V (where DeltaV= V_(f)- V_(i) ). For reversible process P_("ext") = P_("int") +- dP ~~ P_("int") , so for reversible isothermal process W= -nRT ln (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)= 8 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 against a constant pressure of 20 bar until P_("gas") = P_("ext") . Total work done on the gas in two stage compression is

An ideal gas of specific heat ratio gamma with volume and pressure P is compressed to increase the pressure by DeltaP . If the change in volume is Delta V_1 in an isothermal process and Delta V_2 in an adiabatic process, then

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