Transcript Thermal Expansion

Equation of State
Vn
1
V
p
pT
pV  nRT
Ideal-gas Equation
Where:
P = pressure (Pa)
V = volume (m3)
n = number of moles (mols)
R = ideal gas constant
R= 8.31451 J/mols.K
R= 0.08206 L.atm/mol.K
T = temperature (K)
Equation of State
pV  nRT
Where:
P = pressure (Pa)
V = volume (m3)
n = number of moles (mols)
R = ideal gas constant
R= 8.31451 J/mols.K
R= 0.08206 L.atm/mol.K
T = temperature (K)
Example 1: Volume of gas at STP: The condition called standard
temperature and pressure (STP) for a gas is defined to be a temperature of
0oC=273.15 K and a pressure of 1atm = 1.013x105 Pa. If you to keep a mole
of an ideal gas in your room at STP, how big a container you need?
Ans: 22.4L
Example 2: Compressing gas in an
automobile engine. In an automobile
engine, a mixture of air and gasoline is
compressed in the cylinder before being
ignited. A typical engine has a compression
ratio of 9.00 to 1; this means that gas in the
cylinders is compressed to 1/(9.00) of its
original volume (see Fig.). The initial
pressure is 1.00 atm, and the initial
temperature is 27oC. If the pressure after
compression is 21.7 atm, find the
temperature of compressed gas, Ans: 450oC
Example 1: Mass of air in a scuba tank: A typical tank used for scuba
diving has a volume of 11.0L (about 0.4ft3) and a gauge pressure, when full,
of 2.10x107 Pa (about 3000psig). The “empty” tank contains 11.0L of air at
21oC and 1atm (1.013x105 Pa). When the tank is filled with hot air from a
compressor, the temperature is 42oC and the gauge pressure is 2.10x107
Pa. What mass of air is added? (Air is a mixture of gases, about 78%
nitrogen, 21% oxygen, and 1% miscellaneous; its average molar mass is
28.8 g/mol=28.8x10-3kg/mol.)
Ans: 2.54 kg.
pV diagram
Isotherm, or contant temperature
curves, for a constant amount of an
ideal gas. For each curve, the
product pV=nRT is constant, so p is
proportional to 1/V; the
proportionality constant increases
with increasing T.
A pV-diagram for a non-ideal gas, showing
isotherms for temperatures above and
below the critical temperature Tc The
liquid-vapor equilibrium region is shown as
a green shaded area. At still lower
temperatures the material might undergo
phase transitions from liquid to solid or
from gas to solid.
Seat Work 1: A 20.0 L tank contains 0.225 kg of Helium at 18.0 oC.
The molar mass of helium is 4.00 g/mol. a) How many moles of helium
are in the tank, in pascals and in atmosphere?
Answer: a) 56.2 mol b) 6.81x106 Pa =67.2 atm
Seat Work 2: A cylindrical tank has a tight-fitting piston that allows the
volume of the tank to be changed. The tank originally contains
0.110m3 of air at a pressure of 3.4 atm. The piston is slow ly pulled out
until the volume of the gas is increased to 0.390 m3. If the temperature
remains constant, what is the final value of the pressure?
Answer: 0.959 atm
Seat Work 3: A large cylindrical tank contains 0.750 m3 of nitrogen
gas at 27 oC and 1.50x105 Pa (absolute pressure). The tank has a
tight-fitting piston that allows the volume to be changed. What will
be the pressure if the volume is decreased to 0.480 m3 and
temperature is increased to 157oC?
Answer: 3.36x105 Pa atm