HW4_Chapter 19
19-2:
Q.
Consider an ideal gas that occupies 2.50 dm
3
at a pressure of 3.00 bar. If the gas is
compressed isothermally at a constant external pressure,
P
ext
, so that the final volume is 0.500
dm
3
, calculate the smallest value
P
ext
can have. Calculate the work involved using this value of
P
ext
.
A.
Since the gas is ideal, we can write
3
1
1
2
3
2
(3.00
)(2.5
)
15.0
0.500
PV
bar
dm
P
bar
V
dm
The smallest possible value of
P
ext
is
P
2
. The work done in this case is (Equation 19.1)
1
1
3
3
1
1
8.3145
(15.0
)( 2.0
)
3000
0.083145
ext
J mol
K
w
P
V
bar
dm
J
bar dm
mol
K
19-6:
Q.
Calculate the minimum amount of work required to compress 5.00 moles of an ideal gas
isothermally at 300 K from a volume of 100 dm
3
to 40.0 dm
3
.
A.
We note that the minimum amount of work required is the amount of work needed to
reversibly compress the gas, so we can write Equation 19.2 as
2
min
1
ln
rev
V
w
w
nRT
V
1
1
(5.00
)(8.315
)(300
)ln0.4
11.4
mol
J mol
K
K
kJ
19-17:
Q.
Show that
/
2
2
1
1
P
R C
T
P
T
P
for a reversible adiabatic expansion of an ideal gas.
A.
For an ideal gas,
V
P
C
R
C
and

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