Lecture 16 - Temperature and Kinetic Theory
The SI unit of temperature is K (Kelvin). We can convert a temperature from Celsius to Kelvin by adding 273 (not exact, see below):
Using different types of gases, different amount, and running the experiment at different pressure all lead to the same temperature of zero volume, so clearly there is something special about −273.15∘C, which we now call absolute zero. The Kelvin scale is defined so that absolute zero is exactly 0K.
One can see in the Kelvin scale, V∝T.
An ideal gas is a gas of point particles which has no other interactions besides collision among molecules. There is no intermolecular force. An ideal gas obeys the ideal gas law:
P | Pa |
V | m3 |
T | K |
n | mol |
Real gas molecules have non-zero volume (i.e. not point particles), and there is generally intermolecular force. However, for most gases at room temperature the size of the gas molecules are small compared to the whole volume of the gas, and the molecules are usually separated far enough for the intermolecular forces to be negligible (except when the gas is close to phase transition) so the ideal gas law usually works very well.
n and N are related to each other via N=nNA, where NA=6×1023 is the Avogadro's number. NA is the number of molecules in 1 mole of gas.
A good analogy to Avogadro's number is the concept of dozen used in a bakery. You can think of NbakerA=12 for a baker. So if you buy 3 dozens of donuts, it means you are buying N=nNA=(3)(12)=36 donuts.
Number of moles, n | Number of molecules, N=nNA |
---|---|
1 | 6×1023 |
2 | 12×1023 |
3 | 18×1023 |
4 | 24×1023 |
Number of dozens, n | Number of donuts, N=nNA |
---|---|
1 | 12 |
2 | 24 |
3 | 36 |
4 | 48 |
The SI unit for volume is m3. Unit conversion is a very basic skill for a science major. Make sure you know how to convert units to and from cm3 and L (liter) correctly or you will be penalized heavily. Here is a quick reminder: 1m=100cm⇒1m2=(100cm)2=104cm2⇒1m3=(100cm)3=106cm3 Using the above, we get: 1cm3=10−6m31L=1000cm3=1000×10−6m3=10−3m3
The SI unit of pressure is Pa (Pascals), which is equivaldent to N/m2.
A common non-SI unit for pressure is atm, or "atmospheric pressure". To convert to SI unit, use 1atm≈105Pa.
The term STP stands for standard temperature and pressure, meaning T=0∘C and P=1atm.
An alternative way of writing the ideal gas law is PV=NkT, where k=1.38×10−23J/K is the Boltzmann constant. Compare with the version presented above PV=nRT, we could see: NkT=nRT⇒Nk=nR⇒k=nRN=nRnNA=RNA=1.38×10−23J/K
A useful equation derived from the ideal gas law is:
Name | Symbol | Unit | Meaning |
---|---|---|---|
Pressure | P | Pa | force per unit area |
Volume | V | m3 | size of a gas |
Temperature | T | K | how hot an object is |
Avogadro's number | NA=6×1023 | none | number of molecules in one mole |
Number of moles | n | mol | amount of molecules as multiples of NA |
Number of molecules | N | none | N=nNA |