ES330 Assignment 1 Solutions
Chapters 2 and 3
Due Date: Thursday September 2, 2010
1
Similar to Problem 27 in Text
The pressure in an automobile tire depends on the temperature of the air in the tire. When the
air temperature is 25
o
C
, the pressure gage reads 225
kPa
.
If the volume of the tire is 0.035
m
3
,
determine the pressure rise in the tire when the air temperature in the tire rises to 55
o
C
. Also,
determine the amount of air that must be bled off to restore pressure to its original value at this
temperature. Assume the atmospheric pressure to be 100
kPa
.
Solution
(1)
Find the Change in Pressure:
We can assume the air behaves ideally under these conditions, and can therefore apply
the Ideal Gas Law:
Pν
=
RT
(1)
ν
=
RT
1
P
1
=
RT
2
P
2
(2)
Here,
ν
is the specific volume.
This is assuming that the volume of the tire does not
change with varying temperature. We can now simplify the equation to:
T
1
P
1
=
T
2
P
2
(3)
The temperatures must be converted into Kelvin to obtain the correct solution:
T
1
=25
o
C
+ 273.15 = 298.15K
T
2
=55
o
C
+ 273.15 = 328.15K
The pressure must be converted from gage to absolute:
P
1
,atm
=
P
1
,gage
+
P
atm
=225
kPa
+100
kPa
=325
kPa
Therefore, solving for
P
2
in Equation 3:
P
2
=
P
1
T
2
T
1
=
(325
kPa
)(328
.
15
K
)
298
.
15
K
= 358
kPa
(4)
To get the pressure change:
ΔP=
P
1

P
2
= 358
kPa
 325
kPa
ΔP=33
kPa
1
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(2)
Determine How Much Air Should be Released to Restore 225
kPa
:
To determine how much air should be released, the original mass in the tire must be
calculated. This can be done by applying the ideal gas law to calculate the mass (either
at 25
o
C
and 325
kPa
or
at 55
o
C
and 358
kPa
). The gas constant for air is also needed:
R
air
= 0
.
2870
kJ
Kg
*
K
= 0
.
2870
kPa
*
m
3
Kg
*
K
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 Fall '10
 Bohl
 Force

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