Page 87 - Physical chemistry eng

64 CHAPTER 3 The Importance of State Functions: Internal Energy and Enthalpy

Vocabulary

cyclic rule internal pressure isothermal compressibility
exact differential isenthalpic Joule-Thomson coefficient
heat capacity at constant pressure isobaric volumetric thermal expansion Joule-Thomson experiment
heat capacity at constant volume coefficient partial derivatives

Concept Problems

Q3.1 The heat capacity C P, m is less than C V, m for H O(l) Q3.12 Why are q and w not state functions?
2
near 4°C. Explain this result. Q3.13 Why is the equation ¢H = T f C (T) dT =
1 T i P
Q3.2 What is the physical basis for the experimental result n T f C (T) dT valid for an ideal gas even if P is not con-
1 T i P,m
that U is a function of V at constant T for a real gas? Under stant in the process? Is this equation also valid for a real gas?
what conditions will U decrease as V increases? Why or why not?
Q3.3 Why didn’t Joule change his experiment to make Q3.14 What is the relationship between a state function and
C surroundings >C system L 0.001 to increase the sensitivity of an exact differential?
the apparatus?
Q3.15 Is the following statement always, never, or some-
Q3.4 Why does the relation C 7 C V always hold for a times valid? Explain your reasoning: ¢H is only defined for a
P
gas? Can C 6 C V be valid for a liquid? constant pressure process.
P
Q3.5 Why can q be equated with a state function if q is not Q3.16 Is the following statement always, never, or sometimes
V
a state function? valid? Explain your reasoning: a thermodynamic process is
Q3.6 Explain without using equations why (0H>0P) T is completely defined by the initial and final states of the system.
generally small for a real gas. Q3.17 Is the following statement always, never, or sometimes
Q3.7 Why is it reasonable to write dH L C dT + VdP valid? Explain your reasoning: q = 0 for a cyclic process.
P
for a liquid or solid sample? Q3.18 The molar volume of H O(l) decreases with increas-
2
Q3.8 Refer to Figure 1.10 and explain why (0U>0V) T is ing temperature near 4°C. Can you explain this behavior
generally small for a real gas. using a molecular level model?
Q3.9 Can a gas be liquefied through an isenthalpic expan- Q3.19 Why was the following qualification made in
sion if m J-T = ? 0 Section 3.7? Note that Equation (3.47) is only applicable to a
Q3.10 Why is q =¢U only for a constant volume process in which there is no change in the phase of the sys-
v
process? Is this formula valid if work other than P–V work tem, such as vaporization or fusion, and in which there are no
is possible? chemical reactions.
Q3.11 Classify the following variables and functions as Q3.20 Is the expression ¢U = T 2 C dT = n T 2 C V, m dT
V
V
1 T 1
intensive or extensive: T, P, V, q, , U, H. only valid for an ideal gas if V is constant? 1 T 1
w
Numerical Problems

Problem numbers in red indicate that the solution to the prob- In this equation, T is the absolute temperature in kelvin. The
n
n
lem is given in the Student’s Solutions Manual. ratios T /K ensure that C P, m has the correct dimension.
w
P3.1 Obtain an expression for the isothermal compressibil- Assuming ideal gas behavior, calculate q, , ¢U , and ¢H if
ity k =-1>V (0V>0P) T for a van der Waals gas. 1.50 moles of SO (g) is heated from 22.5°C to 1140.°C at a
2
w
constant pressure of 1 bar. Explain the sign of .
P3.2 Use the result of Problem P3.26 to show that
(0C >0V) T for the van der Waals gas is zero. P3.4 Use the relation (0U>0V) T = T(0P>0T) V - P and
V
the cyclic rule to obtain an expression for the internal pres-
of SO (g) is described
P3.3 The molar heat capacity C P, m 2
by the following equation over the range sure, (0U>0V) T , in terms of P, , T, and . kb
300 K 6 T 6 1700 K : P3.5 A mass of 34.05 g of H O(s) at 273 K is dropped into
2
185 g of H O(l) at 310. K in an insulated container at 1 bar of
2
C P,m T T 2
-3
-7
= 3.093 + 6.967 * 10 - 45.81 * 10 pressure. Calculate the temperature of the system once equi-
R K K 2 librium has been reached. Assume that C P, m for H 2 O is con-
T 3 stant at its values for 298 K throughout the temperature range
-9
+ 1.035 * 10 3 of interest.
K