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")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 :
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 :
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)`
Text Solution
Verified by Experts
The correct Answer is:
C
In isothermal compression is
`w_("One-stage")gtw_("Two-stage")gtw_("Reversible")`
`w_("One-stage")gtw_("Two-stage")gtw_("Reversible")`
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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") Total work done on the gas in two stage 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")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") Work done on the gas in single stage compression is :
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