General Chemistry Principles, Patterns, and Applications, 2011

a. Convert the temperature of the surface of the sun (5800 K) and the boiling points of
gold (3080 K) and liquid nitrogen (77.36 K) to °C and °F.
b. A student is ill with a temperature of 103.5°F. What is her temperature in °C and K?
Solution:
a.
b.
Sun : Gold : N2 :
5800 K = (5800 - 273.15)°C
= 5527°C°F = 9°F5°C(5527°C)
+ 32°F = 9981°F3080 K
= (3080 - 273.15)°C = 2807°C°
c.
°C = 5°C9°F(103.5°F - 32°F) = 40°CK = 40°C + 273.15 = 313 K
Unit Conversions: Dimensional Analysis
In Essential Skills 2, you learned a convenient way of converting between units of measure, such as from
grams to kilograms or seconds to hours. The use of units in a calculation to ensure that we obtain the final
proper units is called dimensional analysis. For example, if we observe experimentally that an object’s
potential energy is related to its mass, its height from the ground, and to a gravitational force, then when
multiplied, the units of mass, height, and the force of gravity must give us units corresponding to those of
energy.
Energy is typically measured in joules, calories, or electron volts (eV), defined by the following
expressions:
1 J = 1 (kg·m 2 )/s 2 = 1 coulomb·volt1 cal = 4.184 J1 eV = 1.602 × 10 −19 J
To illustrate the use of dimensional analysis to solve energy problems, let us calculate the kinetic energy in
joules of a 320 g object traveling at 123 cm/s. To obtain an answer in joules, we must convert grams to
kilograms and centimeters to meters. Using Equation 5.4, the calculation may be set up as follows:
KE = 12mv2 = 12 g ( )(kgg)[(cms)(mcm)]2
= (g)(kgg)(cm2s2 / m2cm2) = kg ×m2s2
= 12320g(1 kg1000g)[(123cm1 s)(1 m100cm)]2
= 0.320 kg2[123 ms( 100)]2
= 120.320 kg[ ( 123)2m2s2( 100)2] = 0.242(kg × m2) / s2 = 0.242 J
Saylor URL: http://www.saylor.org/books
Saylor.org
491