1
Homework 3 Answer
(Due 02/04/2011 Friday)
P2.3, P2.7, P2.8, P2.11, P2.16, P2.19, P2.20, P2.21, P2.23, P2.25, P2.26
P2.3)
3.00 moles of an ideal gas are compressed isothermally from 60.0 to 20.0 L using a constant
external pressure of 5.00 atm. Calculate
q,
w,
U,
and
H.
The work against a constant pressure:
J
10
03
.
2
m
10
60
m
10
20
Pa
101325
5
V
p
w
4
3
3
3
3
external
0
U
and
0
H
since
0
T
and
PV
U
H
J
10
03
.
2
w
q
4
P2.7)
For 1.00 mol of an ideal gas,
P
external
=
P
= 200.0
10
3
Pa. The temperature is changed from
100.0°C to 25.0°C, and
C
V,m
= 3/2
R.
Calculate
q, w,
U,
and
H.
J
935
K
373

K
98
2
mol
K
J
314472
.
8
mol
.0
1
2
3
T
C
n
U
1

1

m
V,
J
559
1
K
373

K
98
2
mol
K
J
314472
.
8
mol
.0
1
2
5
T
R
C
n
T
C
n
H
1

1

m
V,
m
p,
J
H
1559
q
P
J
624
)
1559
(
)
935
(
q

U
P
J
J
w
P2.11)
Calculate
H
and
U
for the transformation of 1.00 mol of an ideal gas from 27.0°C and 1.00
atm to 327°C and 17.0 atm if
C
P
,
m
20.9
0.042
T
K
in units of J K
1
mol
1
For an ideal gas,
H is given by:
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2
K
600
K
300
T
T
m
p,
dT
K
T
0.042
20.9
n
dT
C
n
Δ
H
f
i
J
10
11.94
J
10
67
5.
J
10
6.27
J
T
0.021
J
K
300
K
600
20.9
Δ
H
3
3
3
K
600
K
300
2
J
10
9.45
K
300
K
mol
J
8.314472
mol
1
J
10
94
.
1
1
Δ
T
R
n
Δ
H
pV
Δ
Δ
H
Δ
U
3
1

1

3
P2.12)
Calculate
w
for the adiabatic expansion of 1.00 mol of an ideal gas at an initial pressure of 2.00
bar from an initial temperature of 450. K to a final temperature of 300. K. Write an expression for the
work done in the isothermal reversible expansion of the gas at 300. K from an initial pressure of 2.00
bar. What value of the final pressure would give the same value of
w
as the first part of this problem?
Assume that
C
P,m
= 5/2
R.
J
10
1.87
K
50
1
mol
K
J
314472
.
8
mol
2
3
T
R
C
n
U
w
3
1

1

m
p,
ad
p
p
ln
T
R
n
w
f
i
reversible
and
T
R
n
w
p
p
ln
reversible
f
i
7497
.
0
K
00
3
mol
K
J
314472
.
8
mol
1
J
10
1.87
T
R
n
w
p
p
ln
1

1

3
reversible
f
i
12
.
2
p
p
f
i
i
f
p
p
0.944
2.12
bar
P2.15)
An ideal gas undergoes an expansion from the initial state described by
P
i
,
V
i
,
T
to a final state
described by
P
f
,
V
f
,
T
in (a) a process at the constant external pressure
P
f
and (b) in a reversible process.
Derive expressions for the largest mass that can be lifted through a height
h
in the surroundings in these
processes.