Section 3 - Temperature scale conversions
3.1 Convert each of the following temperatures to the indicated scale: (a) 100.00 K to the Celsius scale; (b) 100.00 K to the
Fahrenheit scale; (c) 72°F to the Celsius scale; and (d) í273.15°C to the Fahrenheit scale.
(a) °C
(b) °F
(c) °C
(d) °F
3.2 What Celsius temperature is the same when converted to Fahrenheit? (There is only one such temperature.)
°
3.3 An iron rod is heated from 66.0°F to 280°F. Express the increase in temperature in Celsius.
°C
3.4 In 1731 the French scientist Rene Reaumur proposed the Reaumur temperature scale. The reference points for his scale
were the freezing and boiling points of water (0°R and 80.0°R respectively). Like the Fahrenheit scale in northern Europe, his
scale was widely used in France until the 1960's, when the Celsius scale was officially adopted. (a) Convert 37.0°C to
Reaumur. (b) Convert 56.5°F to Reaumur. (c) Convert 256 K to Reaumur.
(a) °R
(b) °R
(c) °RSection 8 - Thermal expansion: linear
8.1 The plumbing in an old house uses lead pipes (which are now considered hazardous). Hot water is run through a section of
pipe, increasing its temperature from 19.4°C to 36.8°C. If the pipe is initially 3.90 m in length, what is the change in the length
of the pipe?
m
8.2 A square copper plate has a circular hole in its center. Each side of the plate is 23.52 cm, and the radius of the circular hole is
7.827 cm. If the plate's temperature increases 174.3 K, what are the new lengths of (a) the side of the plate and (b) the radius
of the hole? Express your answers to four significant digits.
(a) cm
(b) cm
8.3 A metal rod is 2.673 m long at 23.25°C. When its temperature is increased to 168.4°C, the length of the rod is 2.681 m. What
is the metal's coefficient of linear expansion? Express your answer to four significant digits.
1/C °
8.4 The aptly-named Steel Bridge over the Willamette River in Portland, Oregon, has a central span steel truss that is 64.1 m
long. What is its change in length over the year from the average minimum annual temperature of 0.90°C to the average
maximum of 26.3°C? Use a coefficient of linear expansion of 1.17×10í^5 (1/C°).
m
8.5 A ring of silver has an inside diameter of 2.355 cm at a temperature of
23.48°C. A steel rod has a diameter of 2.361 cm. To what temperature should you raise the ring so it will just slip onto the
rod? Assume the rod does not change temperature. Express your answer to four significant digits.
°C
8.6 An aluminum ring has an inside diameter of 1.793 cm, and an iron rod has a diameter of 1.798 cm, both at 18.73°C. If you
increase the temperature of both the ring and the rod, at what common temperature will the ring just slip onto the rod?°C
8.7 An aluminum beam shows a length of L meters as measured with a steel measuring tape, with both the beam and the tape at
a temperature Ti. The temperature (of both the beam and the measuring tape) then increases by ǻT. Develop an expression
for the value the tape now shows for the length of the beam. Hint: Find out how long a meter becomes on the steel measuring
tape, find the new length of the aluminum beam, then think about how to combine the two results.8.8 A clock is designed with a simple pendulum, consisting of a mass at the end of an aluminum rod, whose period is supposed
to be equal to one second. The clock is designed to keep accurate time at 20.0°C, but is operated at a constant temperature
of í80.0°C. (a) Will the clock run fast or slow? Explain. (b) How many periods will the pendulum go through before the clock is
off by 1.00 s? (The coefficient of linear expansion of aluminum is 2.31×10í^5 1/C°.)
(a) Fast Slow
(b) periods(^356) Copyright 2007 Kinetic Books Co. Chapter 18 Problems