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 :
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 :
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 :
A
36
B
72
C
144
D
None of these
Text Solution
Verified by Experts
The correct Answer is:
C
`w_("irr")=-P_("ext")(V_(2)-V_(1))`
`=-20((nRT)/(P_(2))-(nRT)/(P_(1)))`
= 144 bar-L
`=-20((nRT)/(P_(2))-(nRT)/(P_(1)))`
= 144 bar-L
Topper's Solved these Questions
Similar Questions
Explore conceptually related problems
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") 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")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 :
2 mole of an ideal gas undergoes isothermal compression along three different paths (i) reversible compression from P_(i)=2 bar and V_(i)=4L" 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") . Calculate the work (in bar. L) for each of these processes and for which of the irreversible processes is the magnitude of the work greater ? [Given : R = 0.08 bar. L/mole.K]
Draw p-V diagram of reversible process.
The ratio of slopes of P-V plots for reversible adiabatic process and reversible isothermal process of an ideal gas is equal to :
The P-V diagram of a gas system undergoing cyclic process is shown here. The work done during isobaric compression is
For a reversible process at T = 300K, the volume is increased from V_(i)=1L to V_(f)=10L . Calculate Delta H if the process is isothermal -