1
ME 201
Thermodynamics
Conservation of Mass Practice Problems
1.
A human being can blow air out of their mouth at a rate of 10
4
kg/s. How long will
it take for this human to blow up a balloon to a volume of 5 x 10
4
m
3
? The air may
be taken to be at 311 K and 110 kPa.
Solution:
This is a conservation of mass problem with one inflow and no outflows
and zero initial mass. Writing the conservation of mass, we have
in
initial
final
m
t
m
m
&
=
∆

Assuming that the initial mass is zero and solving for the time period, we have
m
m
t
in
final
&
=
∆
For the final mass, we have
v
V
m
final
final
=
We will determine the specific volume, v, for air from the ideal gas equations, or
/kg
m
0.81
(110)
1)
(0.287)(31
P
RT
v
3
=
=
=
Then
kg
10
x
6.17
0.81
10
x
5
m
4

4
final
=
=
So that
s
6.2
10
10
x
6.17
t
4

4
=
=
∆
2.
Consider a 40 gallon hot water heater. Over a fifteen minute time period hot water
flows out of the hot water heater at 0.75 kg/s and cold water at 0.5 kg/s flows into
the hot water heater. How full (in percent) is the hot water heater at the end of
fifteen minutes? You may take the water temperature to be 85ºC.
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 Spring '06
 SOMERTON
 Litre, hot water heater

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