Ideal Gas Equation in Different Thermodynamic Condition

In the previous post, we have discussed about ideal gas equation and real gas equation. We have also discussed about some extra parameters which converts ideal gas equation into real gas equation.

Now in this post, we are going to analysis ideal gas equation for different condition such as constant pressure, constant volume, isothermal ( constant temperature ), adiabatic & isentropic.

Let’s get started………..  ( HERE ONE THING PUT IN YOUR MIND WHICH IS THAT IDEAL GAS EQUATION PV=mRT  IS ONLY VALID FOR CLOSED SYSTEM AND REVERSIBLE CYCLES )

1.       CONSTANT PRESSURE PROCESS ( ISOBARIC PROCESS)

In this process pressure is constant so we can say that P=C ( here C is a constant ).

We all know that formula of an ideal gas is PV=mRT.  

Apply above equation for state 1 and state 2 .  so       P₁V₁=MRT₁  & P₂V₂=mRT₂ 

But here P=C so u can write :   V₁/V₂=T₁/T₂   or V/T=C

2.       CONSTANT VOLUME PROCESS ( ISOCHORIC PROCESS)

 In this process pressure is constant so we can say that V=C ( here C is a constant ).

We all know that formula of an ideal gas is PV=mRT.  

Apply above equation for state 1 and state 2 .  so       P₁V₁=MRT₁  & P₂V₂=mRT₂ 

But here V=C so u can write :   P₁/P₂=T₁/T₂   or   P/T=C

3.       CONSTANT TEMPRATURE PROCESS ( ISOBARIC PROCESS)

  In this process pressure is constant so we can say that T=C ( here C is a constant ).

We all know that formula of an ideal gas is PV=mRT.  

Apply above equation for state 1 and state 2 .  so       P₁V₁=MRT₁  & P₂V₂=mRT₂ 

But here T=C so u can write :  P₁ V₁=P₂V₂   or   P V=C

NOTE : Isothermal process is not possible in real life because it is impossible to keep temperature constant for entire process. There is always change of temperature. So isothermal process is only theoretical possible. BUT THERE IS A PROCESS IN WHICH TEMPRATURE IS TAKEN CONSTANT, THIS PROCESS IS QUASISTATIC PROCESS. THIS PROCESS IS VERY SLOW ALMOST STOPPABLE SO THEMPRATURE IS TAKEN CONSTANT IN IT.

Ex: wear of stone on the bank of river is one type of quasistatic because stone is wearing with time but it is very slow that u can’t say that process is even occurring. U will see its result after decades.

4.       ADIABATIC PROCESS

 In this process heat transfer is zero. Condition for this process is PV^ɣ=C ( here C is a constant ).

We all know that formula of an ideal gas is PV=mRT.  

Apply above equation for state 1 and state 2 .  so       P₁V₁=MRT₁  & P₂V₂=mRT₂ 

But here PV^ɣ=C so u can write :   T₂ / T₁ = (V₁/V₂) ^ɣ-1  or T₂ / T₁ = (P₂/ P₁) ^{(ɣ-1 )/ɣ}

5.       POLYTROPIC PROCESS

  Condition for this process is PVⁿ=C ( here C is a constant ).

We all know that formula of an ideal gas is PV=mRT.  

Apply above equation for state 1 and state 2 .  so       P₁V₁=MRT₁  & P₂V₂=mRT₂ 

But here PVⁿ=C so u can write :   T₂ / T₁ = (V₁/V₂) ^n-1  or T₂ / T₁ = (P₂/ P₁) ^{(n-1 )/n}

NOTE : Here all above process can be represented by only one equation which is    PV^k = C , where k show slope of process on p-v diagram. k has different values for different processes.

k = 0 ( for isobaric process )

k =∞ ( for isochoric process)

k=1 ( for isothermal process)

k=ɣ ( for adiabatic process)

k=n( for isentropic process)

CLICK HERE TO KNOW MORE ABOVE THERMODYNAMICS AND PV DIAGRAM