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Example 41
Nitrogen is contained in a pistoncylinder assembly with
an initial volume of 0.4 m
3
, an initial temperature of 20°C,
and a pressure of 300 kPa. The nitrogen expands at
constant pressure while 390 kJ of heat is added. Find the
final temperature and the work done
a) assuming constant specific heats at 20°C
b) using variable specific heat
Solution:
a) For a constant pressure expansion in a closed system,
QH
=∆
Assuming constant specific heats
()
21
p
Qm
cTT
=−
To find the mass, use
3
1
m
VOLUME(N2,
300,
20)
0.29
kg
vP
T
==
=
=
3
1
3
1
0.4m
1.38kg
m
0.29
kg
V
m
v
=
kJ
CP(N2,
20)
1.04
kg K
p
cT
=
⋅
p
Q
TT
mc
=+
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o
2
390kJ
20 C
kJ
1.38kg
1.04
kg K
T
=+
⎛⎞
⎜⎟
⋅
⎝⎠
o
2
292 C
T
=
From the first law for a closed system
UQW
∆=−
WQ U
=−
∆
21
v
WQm
cTT
−
kJ
CV(N2,
20)
0.744
kg K
v
cT
==
=
⋅
o
kJ
0.744
292
20
C
kg K
W
−
⋅
111kJ
W
=
b) In the second part, specific heat is not assumed to be
constant. We begin again with
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 Spring '08
 BORCATASCIUC

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