Page 243 - Schaum's Outline of Theory and Problems of Applied Physics

228 EXPANSION OF SOLIDS, LIQUIDS, AND GASES [CHAP. 19

IDEALGASLAW
Boyle’s law and Charles’s law can be combined to form the ideal gas law:

p 1 V 1 p 2 V 2
=
T 1 T 2
This law is obeyed fairly well by all gases through a wide range of pressures and temperatures. An ideal gas is
one for which pV/T = constant under all circumstances. Although no such gas actually exists, the fact that a
real gas behaves approximately as an ideal one provides a specific target for theories of the gaseous state.
The ideal gas law is further discussed in Chapter 20.

SOLVED PROBLEM 19.10
Nitrogen boils at −196 C. What is this temperature on the absolute scale?
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T K = T C + 273 =−196 + 273 = 77 K

SOLVED PROBLEM 19.11
The surface temperature of the sun is about 6000 K. What is the Celsius equivalent of this temperature?

T C = T K − 273 = 5727 C
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SOLVED PROBLEM 19.12
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Ethyl alcohol freezes at −173 F and boils at 172 F. What are these temperatures on the Rankine scale?
T R = T F + 460 =−173 + 460 = 287 R
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T R = 172 + 460 = 632 R
SOLVED PROBLEM 19.13
To what temperature must a gas sample initially at 0 C and atmospheric pressure be heated if its volume
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is to double while its pressure remains the same?
Since T 1 = 0 C = 273 K and V 2 = 2V 1 , from Charles’s law
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T 1 V 2 (273 K)(2V 1 )
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T 2 = = = 546 K = 273 C
V 1 V 1
SOLVED PROBLEM 19.14
5
The tire of a car contains air at an absolute pressure of 2.4 × 10 Pa when its temperature is 10 C. If the
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tire’s volume does not change, what is the pressure when the temperature is 40 C?
The first step is to convert the temperatures to their absolute equivalents:
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T 1 = 10 + 273 = 283 K T 2 = 40 + 273 = 313 K
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5
Since p 1 = 2.4 × 10 Pa and V 1 = V 2 , from the ideal gas law p 1 V 1 /T 1 = p 2 V 2 /T 2 we have
5
T 2 p 1 (313 K)(2.4 × 10 Pa) 5
p 2 = = = 2.7 × 10 Pa
T 1 283 K