Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Chapter 1 | 31

A = 0.04 m^2

P =?

Patm = 0.97 bar

m = 60 kg

Patm

W = mg

P

FIGURE 1–54

Schematic for Example 1–9, and the

free-body diagram of the piston.

Engine Lungs

FIGURE 1–53

At high altitudes, a car engine

generates less power and a person gets

less oxygen because of the lower

density of air.

EXAMPLE 1–9 Effect of Piston Weight on Pressure in a Cylinder

The piston of a vertical piston–cylinder device containing a gas has a mass
of 60 kg and a cross-sectional area of 0.04 m^2 , as shown in Fig. 1–54. The
local atmospheric pressure is 0.97 bar, and the gravitational acceleration is
9.81 m/s^2. (a) Determine the pressure inside the cylinder. (b) If some heat is
transferred to the gas and its volume is doubled, do you expect the pressure
inside the cylinder to change?

Solution A gas is contained in a vertical cylinder with a heavy piston. The
pressure inside the cylinder and the effect of volume change on pressure are
to be determined.
Assumptions Friction between the piston and the cylinder is negligible.
Analysis (a) The gas pressure in the piston–cylinder device depends on the
atmospheric pressure and the weight of the piston. Drawing the free-body
diagram of the piston as shown in Fig. 1–54 and balancing the vertical
forces yield

Solving for Pand substituting,

(b) The volume change will have no effect on the free-body diagram drawn in
part (a), and therefore the pressure inside the cylinder will remain the same.
Discussion If the gas behaves as an ideal gas, the absolute temperature
doubles when the volume is doubled at constant pressure.

1.12 bar

0.97 bar

1 60 kg 21 9.81 m>s^22

1 0.04 m^22

a

1 N

1 kg#m>s^2

ba

1 bar

105 N>m^2

b

PPatm

mg

A

PAPatm AW

EXAMPLE 1–8 Measuring Atmospheric Pressure
with a Barometer

Determine the atmospheric pressure at a location where the barometric read-
ing is 740 mm Hg and the gravitational acceleration is g 9.81 m/s^2.
Assume the temperature of mercury to be 10 C, at which its density is
13,570 kg/m^3.

Solution The barometric reading at a location in height of mercury column
is given. The atmospheric pressure is to be determined.
Assumptions The temperature of mercury is 10 C.
Properties The density of mercury is given to be 13,570 kg/m^3.
Analysis From Eq. 1–26, the atmospheric pressure is determined to be

Discussion Note that density changes with temperature, and thus this effect
should be considered in calculations.

98.5 kPa

 1 13,570 kg>m^321 9.81 m>s^221 0.74 m2a

1 N

1 kg#m>s^2

ba

1 kPa

1000 N>m^2

b

Patmrgh