An ideal gas is one which follows the following simple equation.
PV= Mrt … (2.9)
where P, V and Tare the pressure, volume and temperature of the gas having mass m, and R is the gas constant. Dividing both sides of equation (2.9) by m we get,
P ( V / m) = RT
Pv = RT where v = V/ m = specific volume of the gas.
In reality, there is no gas which is an ideal gas or perfect gas. However all gases, at a very low pressure and density approach to ideal gas.
If the state of an ideal or perfect gas having mass m is changed from P1, V1, T1 to P2, V2, T2 then from equation (2.9) we get
P1 V1 / T1 = P2 V2 / T2 = Mr = contant
T2 / T1 = P2 V2 / P1 V1
The relationship of eqn. (2.10) may be used for calculating or comparing the temperatures. The relationship given in equation (2.9) is called ideal gas equation of state.
Example 2.1. The temperature t (0c) on a thermometric scale is defined in terms of a property K by the relation
t =a InK+ b.
where a and bare constants. The values of K are found to b~ 1.83 and 6.78 at the ice point and the steam point, the temperature of which are assigned 0 and 100 respectively. Calculate the temperature corresponding to a reading of K equal to 2.42 on the termometer.
SOLUTION. t = a In K + b
K = 1.83 K = 6.78
t = 0 t = 100
0 = a In 1.83 + b
100 = a In 6,78 + b
Solving (2) and (3) for a and b we get
a = 76.355 , b = – 46.14
t = 76.355 In k – 46.14
k = 2.42 => t = 21.34oc.Ans