International Foundation Year (IFY)
Electronic
Engineering
Core
Physics
Module
IFY: Exploring
Physics
(EXPH)
module
Exercise
Worksheet:
Gases
& Kinetic
Theory
Week 6 Exercise Sheet: Gases & Kinetic Theory
Problem 1:
A mass of 135 𝑔𝑔 of a certain element is known to contain 30.1 ∗ 1023 atoms. What is the element?
Problem 2:
A runner weighs 580 𝑁𝑁 (about 130 lb), and 71% of this weight is water. (a) How many moles of
water are in the runner’s body? (b) How many water molecules (𝐻𝐻2 𝑂𝑂) are there? The molecular
weight of water is 18 𝑔𝑔/𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚.
Problem 3:
It takes 0.16 𝑔𝑔 of helium (He) to fill a balloon. How many grams of nitrogen (N2) would be required
to fill the balloon to the same pressure, volume, and temperature?
The molecular weight of Helium and Nitrogen is 4 𝑔𝑔/𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 and 14 𝑔𝑔/𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 respectively.
Problem 4:
An ideal gas at 15.5℃ and a pressure of 1.72 ∗ 105 𝑃𝑃𝑃𝑃 occupies a volume of 2.81 𝑚𝑚3 . (a) How many
moles of gas are present? (b) If the volume is raised to 4.16 𝑚𝑚3 and the temperature raised to
28.2℃, what will be the pressure of the gas?
Problem 5:
Four closed tanks: A, B, C, and D (each contain an ideal gas). The table gives the absolute pressure
and volume of the gas in each tank. In each case, there is 0.10 𝑚𝑚𝑚𝑚𝑚𝑚 of gas. Using this number and
the data in the table, compute the temperature of the gas in each tank.
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Problem 6:
A young male adult takes in about 5.0 ∗ 10−4 𝑚𝑚3 of fresh air during a normal breath. Fresh air
contains approximately 21% oxygen. Assume, the pressure in the lungs is 1.0 ∗ 105 𝑃𝑃𝑃𝑃 and
that air is an ideal gas at a temperature of 310 K, find the number of oxygen molecules in a normal
breath.
Problem 7:
A clown at a birthday party has brought along a helium cylinder, with which he intends to fill
balloons. When full, each balloon contains 0.034 𝑚𝑚3 of helium at an absolute pressure of 1.2 ∗
105 𝑃𝑃𝑃𝑃. The cylinder contains helium at an absolute pressure of 1.6 ∗ 107 𝑃𝑃𝑃𝑃 and has a volume of
0.0031 𝑚𝑚3 . The temperature of the helium in the tank and in the balloons is the same and remains
constant. What is the maximum number of balloons that can be filled?
Problem 8:
On the sunlit surface of Venus, the atmospheric pressure is 9.0 ∗ 106 𝑃𝑃𝑃𝑃, and the temperature is
740𝐾𝐾. On the earth’s surface the atmospheric pressure is 1.0 ∗ 105 𝑃𝑃𝑃𝑃, while the surface
temperature can reach 320 𝐾𝐾. These data imply that Venus has a “thicker” atmosphere at its surface
than does the earth, which means that the number of molecules per unit volume (𝑛𝑛/𝑉𝑉) is greater
on the surface of Venus than on the earth. Find the ratio (𝑛𝑛/𝑉𝑉)𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉/(𝑛𝑛/𝑉𝑉)𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸ℎ.
Problem 9:
A tank contains 0.85 𝑚𝑚𝑚𝑚𝑚𝑚 of molecular nitrogen (N2). Determine the mass (in grams) of nitrogen that
must be removed from the tank in order to lower the pressure from 38 to 25 atm. Assume that the
volume and temperature of the nitrogen in the tank do not change.
1-atm is equivalent to 1.01 ∗ 105 𝑃𝑃𝑃𝑃.
Problem 10:
A tank contains 11.0 𝑔𝑔 of chlorine gas (Cl2) at a temperature of 82℃ and an absolute pressure of
5.60 ∗ 105 𝑃𝑃𝑃𝑃. The mass per mole of Cl2 is 70.9 𝑔𝑔/𝑚𝑚𝑚𝑚𝑚𝑚.
(a) Determine the volume of the tank. (b) Later, the temperature of the tank has dropped to 31℃
and due to a leak, the pressure has dropped to 3.80 ∗ 105 𝑃𝑃𝑃𝑃. How many grams of chlorine gas have
leaked out of the tank?
Problem 11:
Four tanks A, B, C, and D are filled with monatomic ideal gases. For each tank, the mass of an
individual atom and the rms speed of the atoms are expressed in terms of m and vrms, respectively
(see the table). Suppose that 𝑚𝑚 = 3.32 ∗ 10−26 𝑘𝑘𝑘𝑘, and 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 = 1223 𝑚𝑚/𝑠𝑠. Find the temperature
of the gas in each tank.
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Problem 12:
The average value of the squared speed 𝑣𝑣 2 does not equal the square of the average speed (𝑣𝑣)2 . To
verify this fact, consider three particles with the following speeds: 𝑣𝑣1 = 3.0 𝑚𝑚 /𝑠𝑠, 𝑣𝑣2 = 7.0 𝑚𝑚/𝑠𝑠,
and 𝑣𝑣3 = 9.0 𝑚𝑚/𝑠𝑠.
Calculate (a)
(b)
Problem 13:
Ordinary nitrogen gas consists of molecules of N2. Find the mass of one such molecule. The
molecular mass is 28 𝑘𝑘𝑘𝑘/𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘.
Problem 14:
A droplet of mercury has a radius of 0.50 mm. How many mercury atoms are in the droplet? For Hg,
𝑀𝑀 = 202 𝑘𝑘𝑘𝑘/𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 and 𝜌𝜌 = 13 600 𝑘𝑘𝑘𝑘/𝑚𝑚3 .
Problem 15:
Suppose a particular gas molecule at the surface of the Earth happens to have the rms speed for
that gas at exactly 0℃. If it were to go straight up without colliding with other molecules, how
high would it rise? Assume g is constant over the trajectory and mass of the gas is 𝑚𝑚0 = 4.65 ∗
10−26 𝑘𝑘𝑘𝑘. The gas constant is 1.38 ∗ 10−23 𝐽𝐽/𝐾𝐾.
Problem 16:
On a day when atmospheric pressure is 76 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐, the pressure gauge on a tank reads the pressure
inside to be 400 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐. The gas in the tank has a temperature of 9℃. If the tank is heated to 31℃
by the Sun, and if no gas exits from it, what will the pressure gauge read? Assuming the volume also
remain constant during this process.
Note: Gauges on tanks usually read the difference in pressure between inside and outside; this is
called the gauge pressure.
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Problem 17:
An ideal gas has a volume of exactly 1 liter at 1.00 atm and −20℃. To how many atmospheres of
pressure must it be subjected in order to be compressed to 0.500 liter when the temperature is
40℃?
Problem 18:
A certain mass of hydrogen gas occupies 370 𝑚𝑚𝑚𝑚 at 16℃ and 150 𝑘𝑘𝑘𝑘𝑘𝑘. Find its volume at −21℃
and 420 𝑘𝑘𝑘𝑘𝑘𝑘.
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