Confirming Pages
5-1
1
Section 5.7: Example
A tank whose capacity is 0.1 m3 contains helium at a pressure of 1000 kPa and a temperature of 20°C. A rubber weather balloon is inflated from this tank (Fig. 1). The helium
cools as it expands, and when the pressure in the balloon is 100 kPa, which is atmospheric
pressure at that time, the temperature of the helium is −40°C. (The helium has done work
in expanding at the expense of its heat content, and the cooling reflects this loss of heat.)
Find the volume of the inflated balloon.
Solution
Here T1 = 20°C = 293 K, T2 = −40°C = 233 K, V1 = 0.1 m3, p1 = 1000 kPa, and p2 = 100 kPa.
From Eq. 5-10,
T2 p1V1 (233 K)(1000 kPa)(0.1 m3)
V2 5 _______ 5 ______________________ 5 0.8 m3
T1p1
(293 K)(100 kPa)
Because the tank’s capacity is 0.1 m3, the balloon’s volume is (0.8 2 0.1)m3 5 0.7 m3. As the
balloon warms up to the outside temperature, it will continue to expand until the helium
and air temperatures are the same.
p2 100 kPa
T2 40ºC
0.7 m3
V1 0.1 m3
V2 0.8 m3
p1 1000 kPa
T1 20ºC
0.1 m3
0.1 m3
Figure 1 Inflating a weather balloon.
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