Isothermal Process & Isothermal Equation for a perfect gas

Isothermal Process

If the thermodynamic system is perfectly conducting to the surrounding and undergoes a physical process in such a way that its temperature remains constant throughout, then the process is an isothermal process.

It may be defined as:

A change in pressure & volume of gas without any change in its temperature is called an isothermal process or isothermal operation”.

For such a process, the temperature of the system remains constant,

i.e. T = constant   
       
                                                &  △T = 0

Essential Conditions for Perfect Isothermal Process:

1. The wall of the container must be perfectly conducting.
 
2. The process of compression or expansion should be so slow so as to provide time for exchange of heat.
 

The equation of an Isothermal Change:

Using the equation of Vanderwall’s gas:
PV = nRT
If n = 1mol, R = constant, T= constant
then,     PV = K(constant)
This is an equation of Isothermal Change.

Specific Heat Capacity of Isothermal Change:

In an Isothermal change, T = constant

then △T = 0

As the specific heat of the gas is given by:
C = △Q/m△T

∵  △T =0     ∴ C = ∞

Therefore, in an Isothermal process, the specific heat of the gas is infinite.

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