# Ideal gas temperature scale

The
temperatures on this scale are measured using a constant volume thermometer.

Based on the principle that at low pressure, the temperature of the
gas is proportional to its pressure at constant volume.

The relationship between the temperature and pressure of the gas in
the vessel can be expressed as T = a + b.P

Where the values of the constants a and b for a gas
thermometer are determinedย
experimentally.

Once a and b are known, the
temperature of a medium can be calculated from the relation above by immersing
the rigid vessel of the gas thermometer into the medium and measuringย  the gas pressure.

Ideal gas temperature scale can be developed by
measuring the pressures of the gas in the vessel at two reproducible points
(such as the ice and steam points) and assigning suitable values to
temperatures those two points.

Considering that only one straight
line passes through two fixed points on a plane, these two measurements are
sufficient to determine the constants a and
b in the above equation.

If the ice and the steam points are assigned the values 0 and 100
respectively, then the gas temperature scale will be identical to the Celsius
scale.

In this case, the value of the constant a (that corresponds to an absolute
pressure of zero) is determined to be โ273.150C when extrapolated.

The equation reduces to T = bP, and thusย  weย  need to specify the temperature at
only one
ย ย ย  point to define an absolute
gas temperature
scale.

Absolute gas temperature is identical to thermodynamic
temperature in the temperature range in which the gas thermometer can be
used.We can view that thermodynamic temperature scale at this point as an
absolute gas temperature scale that utilizes an ideal gas that always acts as a
low-pressure gas regardless of the temperature.

At the Tenth international conference on weights and measures in
1954, the Celsius scale has been redefined in terms of a single fixed point and
the absolute temperature scale.

The triple point occurs at a fixed temperature and pressure for a
specified substance.

The selected single point is the triple point of water (the state in
which all three phases of water coexist in equilibrium), which is assigned the
value 0.01 C. As before the boiling pointย ย
of water at 1 atm. Pressureย  is
100.0 C.ย  Thus the new Celsius scale is
essentially the same asย  the old one.

On the Kelvin scale, the size of Kelvin unit is
defined as โ the fraction of 1/273.16 of the thermodynamic temperature of the
triple point of water, which is assigned a value of 273.16Kโ. The ice point on
Celsius and Kelvin are respectively 0 and 273.15 K.

Example 1. Consider as a system, the gas in the cylinder shown in the figure.
The cylinder is fitted with a piston on which number of small weights is
placed.ย  The initial pressure is 200ย  kPa, and the initial volume of the gas is
0.04 m2.

1.ย ย ย ย ย ย ย
Let the gas in the cylinder be
heated, and let the volume of the gas increase to 0.1 m3 while the
pressure remains constant. Calculate the work done by the system duringย ย  this process.

ย

2

Wย ย ย  =ย  โซ P dV

1

ย

Since the pressure is constant, we conclude from the
above equation that

ย

2

W = P โซ dV

1

= P(V2โ V1 )

ย  ย  ย  ย  ย  ย  ย  W = 200 kPa *(0.1
โ 0.04)m3
= 12.0kJ