Ideal gas temperature scale ~ MECHTECH GURU

# 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 –273.150C 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 m2.

1.        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 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(V2- V1 )

W = 200 kPa *(0.1 - 0.04)m3 = 12.0kJ

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