1.2 System, Surroundings, and State
1.1.A bomb calorimeter is a sturdy metal vessel in which
samples can be ignited and the amount of heat given off can
be measured as the heat warms up surrounding water. Draw
a rough sketch of such an experimental setup and label (a)
the system and (b)the surroundings.
1.2.Differentiate between a system and a closed system. Give
examples of both.
1.3.Use the equalities listed in Table 1.1 to convert the given
values to the desired units. (a)12.56 L to cm^3 (b)45°C to K
(c)1.055 atm to Pa (d)1233 mmHg to bar (e)125 mL to
cubic centimeters (f)4.2 K to °C (g)25,750 Pa to bar
1.4.Which temperature is higher? (a)0 K or 0°C (b)300 K
or 0°C (c)250 K or 20°C
1.3 & 1.4 Zeroth Law of Thermodynamics;
Equations of State
1.5.A pot of cold water is heated on a stove, and when the
water boils a fresh egg is placed in the water to cook. Describe
the events that are occurring in terms of the zeroth law of
thermodynamics.
1.6.What is the value of F(T) for a sample of gas whose vol-
ume is 2.97 L and pressure is 0.0553 atm? What would the vol-
ume of the gas be if the pressure were increased to 1.00 atm?
1.7.What is the value of F(p) for a sample of gas whose tem-
perature is 33.0°C and volume is 0.0250 L? What tempera-
ture is required to change the volume to 66.9 cm^3?
1.8.Calculate the value of the constant in equation 1.9 for a
1.887-mol gas sample with a pressure of 2.66 bar, a volume
of 27.5 L, and a temperature of 466.9 K. Compare your an-
swer to the values in Table 1.2. Are you surprised with your
answer?
1.9.Show that one value of R, with its associated units, equals
another value of Rwith its different associated units.
1.10.Use the two appropriate values of Rto determine a con-
version between Latm and J.
1.11.Calculations using STP and SATP use (the same? differ-
ent?) value(s) of R. Choose one phrase to make the statement
correct and defend your choice.
1.5 More on Ideal Gases
1.12.Pressures of gases in mixtures are referred to as partial
pressuresand are additive. 1.00 L of He gas at 0.75 atm is
mixed with 2.00 L of Ne gas at 1.5 atm at a temperature of
25.0°C to make a total volume of 3.00 L of a mixture. Assuming
no temperature change and that He and Ne can be approxi-
mated as ideal gases, what are (a)the total resulting pressure,
(b)the partial pressures of each component, and (c)the mole
fractions of each gas in the mix?
1.13.Earth’s atmosphere is approximately 80% N 2 and
20% O 2. If the total atmospheric pressure at sea level is about
14.7 lb/in.^2 (where lb/in.^2 is pounds per square inch, a com-
mon but non-SI unit of pressure), what are the partial pres-
sures of N 2 and O 2 in units of lbs/in.^2?
1.14.The atmospheric surface pressure on Venus is 90 bar
and is composed of 96% carbon dioxide and approximately
4% various other gases. Given a surface temperature of 730 K,
what is the mass of carbon dioxide present per cubic cen-
timeter at the surface?
1.15.What are the slopes of the following lines at the point
x5? at x10? (a)y 5 x 7 (b)y 3 x^2 5 x 2
(c)y7/x.
1.16.For the following function, evaluate the derivatives in
a–f below.F(w, x, y, z) 3 xy^2 w 33
2z
y3
xyw(^2) z 3
(a) xF
w, y, z
(b) wF
w, y, z
(c) yF
w, y, z
(d)
z
x
F
w, y, zw,x,y
(e) x zF
w,x,yw, y, z
(f) w z xF
w, y, zw,x,y^ x,y,z
1.17.Determine the expressions for the following expres-
sions, assuming that the ideal gas law holds.
(a)^ Vp
T, n
(b)^ Vn
T, p
(c) VT
n,p
(d)^
p
T
n,V
(e) np
T, V
1.18.Why do you think that none of the above exercises ask
you to take a derivative with respect to R? Is it the same rea-
son that we do not define the derivative of Rwith respect to
any other variable?
1.19.When a given amount of air is let out of an automobile
tire, it changes its volume and pressure simultaneously, and as
a result of this the temperature of the air changes. Write a de-
rivative that stands for this change. (Hint:it will be a double
derivative as in 1.16e above.)
22 Exercises for Chapter 1
EXERCISES FOR CHAPTER 1