# 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 determined

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 measuring 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 –273.15^{0}C when extrapolated.

The equation reduces to T = bP, and thus we need to specify the temperature at

only one 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 point

of water at 1 atm. Pressure is

100.0 C. Thus the new Celsius scale is

essentially the same as the old one.

On the Kelvin scale, the size of Kelvin unit is

defined as “ the fraction of 1/273.16 of the thermodynamic temperature of the

triple point of water, which is assigned a value of 273.16K”. 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. The initial pressure is 200 kPa, and the initial volume of the gas is

0.04 m^{2}.

1.

Let the gas in the cylinder be

heated, and let the volume of the gas increase to 0.1 m^{3} while the

pressure remains constant. Calculate the work done by the system during this process.

2

*W *= ∫ *P dV*

1

Since the pressure is constant, we conclude from the

above equation that

2

*W *= *P *∫ *dV*

1

= *P*(*V*2– *V*1 )

* W *= 200 *kPa **(0.1

– 0.04)*m*^{3}

= 12.0*kJ*