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Ideal Gas Equation and Absolute Temperature

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Ideal Gas Equation and Absolute Temperature - Lesson Summary

6. LSPH11 – THERMAL PROPERTIES OF MATTER – IDEAL GAS EQUATION AND ABSOLUTE TEMPERATURE
 
 
Thermal properties of different substances are different and the rate of expansion of a substance changes with temperature.
 
That means, the per degree expansion of a liquid is not uniform at all temperatures.
The readings shown by different thermometers may coincide at calibration points but may vary at other temperatures.
 
Due to this, these thermometers are of no use when accurate measurement of temperature is needed. It is experimentally observed that the temperature readings of “gas thermometers” are independent of the gas used. Hence, these are more reliable for the accurate measurement of temperature.
 
A gas thermometer works on the basis of variation in the pressure or volume with the temperature of the gas in it.
 
Boyle`s Law states that, “If the temperature of a given mass of gas is constant, then its pressure is inversely proportional to its volume.”
At constant temperature, T,

Where “P” is the pressure of the gas and “V” is the volume of the gas.
 
According to Charles’ Law, “At a constant pressure, the volume of a given mass of gas is directly proportional to its temperature (T)
 
 
 
On combining Equations (i) and (ii) we get
 
 , This is known as “Ideal Gas Law”
 
 is a generalised “Ideal Gas Equation“, where ‘μ’ is the number of moles of gas and R is 8.31 Joule per mole per kelvin, which is the universal gas constant.
 
The constant volume “ gas thermometer” works on the principle of the Ideal Gas Law.
Since PV is directly proportional to T when the volume of a given sample of gas is constant , its pressure changes linearly with the temperature of the gas.
 
When a graph is plotted between pressure and temperature, a straight line is obtained.

If the density of the gas is low, the graph will be a perfect straight line for all gases over a large temperature range. 
 
 
Let’s look at the pressure temperature graph for different gases at low density.
When extended towards negative temperatures all these straight lines meet at a point represented by the temperature at -273.15 0 C,
i.e., at -273.15 0 C, if the gas is still in the same state, its pressure reduces to zero.
 
In fact, at this temperature, the average kinetic energy of gas molecules becomes zero.
As a result they cease to move and settle at the bottom of the container and the pressure exerted by them reduces to zero.
 
The zero of Kelvin or Absolute Temperature Scale is called Absolute zero. The temperature of a body on the Absolute scale is expressed in Kelvin and is called Absolute Temperature and is represented by the letter “T”. The size of a degree on the Kelvin scale is identical to the size of a degree on the Celsius scale.
 

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