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3.2 Modelling a gas: Ideal gas law
3. Thermal physics
Ideal gas law: pV = NkT
1.
The air in a kitchen has pressure 1.0 x 10
5
Pa and temperature 22
o
C. A refrigerator of internal
volume of 0.36 m
3
is installed in the kitchen. The refrigerator door is closed. The air in the
refrigerator is cooled to 5.0
o
C and the number of air molecules in the refrigerator stays the
same. With the door open the air in the refrigerator is initially at the same temperature and
pressure as the air in the kitchen. Calculate the number of molecules of air in the refrigerator.
2.
An ideal monatomic gas is kept in a container of volume 2.1 x 10
-4
m
3
, temperature 310 K and
pressure 5.3 x 10
5
Pa. The volume of the gas is increased to 6.8 x 10
-4
m
3
at constant
temperature. Calculate the number of atoms in the gas.
3.
A container of volume 3.2 x 10
-6
m
3
is fi lled with helium gas at a pressure of 5.1 x 10
5
Pa and
temperature 320 K. Assume that this same sample of helium gas behaves as an ideal gas.
Show that the number of helium atoms in the container is 4 x 10
20
.
3.2 Modelling a gas: Ideal gas law
3. Thermal physics
Ideal gas law: pV = nRT
1.
Two volcanic chambers, Prometheus and Tvashtar, underneath two different volcanos are
observed. The chambers have the same volume as each other and contains the same number
of molecules of the same type of gas. The temperature of the gas in Prometheus chamber is
1200 K and the temperature of the gas in Tvashtar is 1600 K. The pressure of the gas in
Prometheus chamber is 8.2 kPa. Calculate the pressure of the gas in Tvashtar chamber.
2.
A gas is contained inside a sealed syringe. The plunger is pushed so that the gas is
compressed and its volume reduces as constant temperature. Before compression, the gas
pressure is 100 kPa and the volume of the gas is 7.5 cm
3
. After compression, the volume of
the gas is 5.0 cm
3
. Calculate the pressure of the gas after compression.
3.
A gas is trapped in a manometer. The pressure of the gas is 9.95 x 10
4
Pa and the temperature
is 16
o
C. Calculate the new pressure of the trapped gas if the temperature increases to 32
o
C.
4.
A helium gas cylinder is 0.200 m
3
in volume, and contains 50.0 moles of gas at room
temperature of 293 K. What is the pressure in the cylinder?
5.
What is the mass of argon fi lling an electric light bulb of volume 8.2 x 10
-5
m
3
if the pressure
inside the light bulb is 90 kPa and the temperature of the gas is 340 K.
Standard pressure is
100 kPa, standard temperature is 273 K and the density of argon is 1.56 kg m
-3
.
