Thermodynamics

Robert Boyle discovered experimentally that the volume of a gas in a J−tube apparatus at a constant temperature varied in inverse proportion to the pressure. This is known as Boyle’s law. Boyle’s law may be expressed mathematically as:

(constant temperature) (1.1)

where V and P are the volume and pressure of the gas, respectively. In the early 19th century, Joseph Gay-Lussac, after following the work of Alex-

andre Charles, established that the volume of a gas increases linearly with temperature at constant pressure. Expressed mathematically, Charles’s law states that:

(constant pressure) (1.2)

where is the volume of the gas at 0°C, α is the proportionality constant (or thermal expansion coefficient) for the gas, and t is the temperature (°C). It was found experimentally that α is independent of the nature of the gas and that it has the value of °C-1. Substituting this value into Equation (1.2) yields:

(1.3)

In Equation (1.3), the volume of the gas becomes zero when the temperature is reduced to –273.15°C, which is the absolute zero temperature. The relation between the Celsius degree and the absolute scale (called Kelvin degree) is given by:

(1.4)

V 1 P

∝

V V (1 t) o

= + α

V o

V V 273.15 t 273.15o

=

+ 

T(K) 273.15 t ( C)= + °

The Kelvin degree scale was originally introduced by William Thomson. It is a thermodynamic temperature scale based on the second law of thermodynamics and is identical to the absolute temperature scale based on the above volume expansion arguments. Substituting Equation (1.4) into Equation (1.3) gives:

or (1.5)

where Volume is an extensive property, which is dependent on the quantity of substance

(or substances) present in the system. Therefore, the volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas, n (Avogadro principle). Unlike volume, temperature and pressure are intensive properties and are independent of the amount of material present in the system. Combining Equation (1.1) and Equation (1.5) with the Avogadro principle gives:

or (1.6)

where R is the proportionality constant or gas constant. Equation (1.6) is known as the ideal gas law. The proportionality constant of Equation (1.6) is determined experimentally.