Phys 101
Chapter 11 - Structure of Matter
Temperature Conversion
To convert from a Fahrenheit temperature to a Celsius temperature we have to subtract 32
degrees from the Fahrenheit reading to get to the zero point on the Celsius scale and then adjust
for the different size degrees. The ratio of the size of the degrees is 5/9 so that the equation for
converting Fahrenheit to Celsius is
5 °C
TC =
(TF − 32 °F)
9 °F
where TC and TF are the corresponding temperatures in Celsius and Fahrenheit. Converting from
Celsius to Fahrenheit is just the reverse of this,
9 °F
TF =
TC + 32 °F
5 °C
Exercise: What is the temperature in Celsius when your Fahrenheit thermometer reads 100°F?
5 °C
5 °C
TC =
(TF − 32 °F) =
(100°F − 32 °F) = 37.8 °C
9 °F
9 °F
Practice: What is the temperature in Celsius when your Fahrenheit thermometer reads one-half
this value, or 50°F (Ans: 10°C)
Exercise: Your friend in Belgium writes to you that last summer the temperature in Brugge
reached a high of 40°C. What is this temperature in Fahrenheit?
9 °F
9 °F
TF =
TC + 32 °F=
× 40°C + 32 °F = 104 °F
5 °C
5 °C
Practice: Room temperature in Europe is 20°C. What is it in Fahrenheit? (Ans: 68°F)
The conversion from the Celsius temperature scale to the absolute or Kelvin scale is easy
because the degrees are the same size, that is, 1°C = 1K. You just need to add or subtract 273°.
If you are converting a Celsius reading to a Kelvin reading you add the 273°, ie
TK = TC + 273 °
Going the other way you subtract 273°. To convert from Fahrenheit, you must first convert to
Celsius.
Example: Oxygen boils at 90 K. What is this temperature in Celsius?
TC = TK − 273 ° = 90 K − 273K = −183K
Practice: Room temperature is about 20°C. What is this temperature on the absolute scale?
(Ans: 293 K)
Phys 101
The Ideal Gas Law: A Macroscopic View
The ideal gas law can be written as
PV = NkT
where N is the number of molecules and k is Boltsman's constant. We can rewrite this as
PV
= constant
T
if we agree to keep the amount and type of gas fixed. This means that the three macroscopic
quantities; pressure, volume, and temperature are not all independent of each other. Because
PV/T is a constant and using the subscripts i and f for the initial and final values, we must have
PV
PV
i i
= f f
Ti
Tf
Whenever any one of the quantities is held fixed, it can be cancelled from both sides and we get
a relationship between the other two. This gives us the various gas laws stated in the text.
Example: What happens to the volume of 50cm3 of gas if its temperature is raised from 20°C to
100°C. Assume that the pressure remains the same.
Canceling the pressure (Pi=Pf) and solving for the final volume, we have
V f = Vi
Tf
Ti
= 50cm3 ×
373K
= 63.7 cm3
293K
Note that temperatures must be expressed in Kelvin when using any of theses relations..