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If the boundary of system moves by an in...

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:

A

9.212

B

36.848

C

18.424

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Work done `= -2.303 n TR "long" (V_(2))/(V_(1))`
`= -2.303 xx 0.083 xx 2 xx ((P_(i)V_(i))/(nR)) ."log" (V_(f))/(V_(i))`
`= -2.303 xx 0.083 xx 2 ((2 xx 8)/(2 xx 0.083)) "log" (2)/(20)`
= 36.848 bar Lt
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Knowledge Check

  • 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

    A
    `w_(1) gt w_(2) gt w_(3)`
    B
    `w_(3) gt w_(2) gt w_(1)`
    C
    `w_(2) gt w_(3) gt w_(1)`
    D
    `w_(1) = w_(2) = w_(3)`

  • 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") Total work done on the gas in two stage compression is

    A
    40
    B
    80
    C
    16
    D
    none of these

  • 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") . Work done (in bar-L) on the gas in reversible isothermal compression is:

    A
    9.212
    B
    36.848
    C
    18.424
    D
    None of these

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