(a) What is the final temperature when the two become equal? Assume that coffee has the same specific heat as water.
(b) The first time a student solved this problem she got an answer of 88 °C. Explain why this is clearly an incorrect answer.Solution
(a) because of the law of conservation of energy, we write:
q
spoon
+
q
coffee
= 0
q
spoon
= –
q
coffee
c
spoon
×
m
spoon
× Δ
T
=
c
coffee
×
m
coffee
× Δ
T
0.88 J/g °C × 45 g × (
T
f
– 24 °C)
= –4.184 J/g °C × 180 g × (
T
f
– 85 °C)
39.6
T
f
– 950.4 = –753.12
T
f
+ 64,015
753.12
T
f
+ 39.6
T
f
= 64,015 + 950.4
792.7
T
f
= 64,965.4
T
f
= 82 °C; (b) The temperature of the coffee cannot increase when a colder spoon is placed in it.
26. When 50.0 g of 0.200 M NaCl(
aq
) at 24.1
C is added to 100.0 g of 0.100 M AgNO
3
(
aq
) at
24.1
C in a calorimeter, the temperature increases to 25.2
C as AgCl(
s
) forms. Assuming the
specific heat of the solution and products is 4.20 J/g
C, calculate the approximate amount of
heat in joules produced.
Solution

q
=
cm
Δ
T
= 4.20 J/g °C × 150 g × (25.2 – 24.1) °C = 693 J
30. When 1.0 g of fructose, C
6
H
12
O
6
(
s
), a sugar commonly found in fruits, is burned in oxygen in
a bomb calorimeter, the temperature of the calorimeter increases by 1.58
C. If the heat capacity
of the calorimeter and its contents is 9.90 kJ/
C, what is
q
for this combustion?
Solution
q
comb
+
q
cal
= 0
q
comb
= –
q
cal
= –9.90 kJ/°C (1.58 °C) = –15.6 kJ
The negative sign indicates that this was reaction exothermic, as expected. The mass did not
directly enter into the calculation because the heat capacity of the system is calculated on a kJ/°C
basis. The mass of the calorimeter is constant.
34. A teaspoon of the carbohydrate sucrose (common sugar) contains 16 Calories (16 kcal). Whatis the mass of one teaspoon of sucrose if the average number of Calories for carbohydrates is 4.1 Calories/g?
36. A pint of premium ice cream can contain 1100 Calories. What mass of fat, in grams and
pounds, must be produced in the body to store an extra 1.1 × 10
3
Calories if the average number
of Calories for fat is 9.1 Calories/g?
Solution
The average heat of combustion of fats is –9.1 kcal/g = –9.1 Calories/g:
2
1.0 g
Mass = 1100 Calories
= 121 g
1.2
10
9.1 Calories
10 lb
Mass
121 g
0.27 lb
453.6 g
.
38. Which is the least expensive source of energy in kilojoules per dollar: a box of breakfast
cereal that weighs 32 ounces and costs $4.23, or a liter of isooctane (density, 0.6919 g/mL) that
costs $0.45? Compare the nutritional value of the cereal with the heat produced by combustion of
the isooctane under standard conditions. A 1.0-ounce serving of the cereal provides 130 Calories.
Solution
Convert ounces to grams and liters to grams, and then find the cost per gram. Determine the heat
of combustion of isooctane on a per gram basis, and compare it with the cost of the heat
produced by cereal.

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- Chemistry, Thermodynamics, Enthalpy, g C