1) The temperature of the gas in state B is 1200 K
2) The work done by the gas from A to B is 4000 J
3) The work done by the gas from B to C is -5546 J
Explanation:
1)
The temperature of the gas when it is in state B can be found by using the ideal gas equation:
where
is the pressure in state A
is the volume in state A
is the temperature in state A
is the pressure in state B
is the volume in state B
is the temperature in state B
Solving for ,
2)
The work done by a gas during an isobaric transformation (as the one between A and B) is
where
p is the pressure (which is constant)
is the final volume
is the initial volume
Here we have:
is the volume in state A
is the volume in state B
Substituting,
3)
During an isothermal expansion, the produce between the pressure of the gas and its volume remains constant (Boyle's law), so we can write:
where
is the pressure in state B
is the volume in state B
is the pressure in state C
is the volume in state C
Solving for ,
The work done by a gas during an isothermal transformation is given by
(1)
where
n is the number of moles
is the gas constant
T is the constant temperature (in this case, )
are the final and initial volume, respectively
The number of moles of the gas can be found as
So now we can use eq.(1) to find the work done by the gas from B to C:
And the work is negative because the gas has contracted, so the work has been done by the surrounding on the gas.
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