What do you mean by equation of state of system?

The equation of a homogeneous system at any time is described in terms of three thermodynamic parameters namely pressure, volume and temperature. 

The mathematical relation between these parameters is called the equation of state of the thermodynamic system. 
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What is process?

A thermodynamic process is a course during which the thermodynamic state of the body changes.
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What are the thermodynamic variables?


Thermodynamic variables are the parameters that completely define the thermodynamic state of the system.

For e.g. pressure, volume, temperature, internal energy, entropy, enthalpy etc are thermodynamic variables. 
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Is heat and work a path function?

Yes, heat and work are path functions.

Rate of heat transfer depends on the path taken. 
The amount of work done also is path-dependent. 
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Is internal energy a path function?

Internal energy is not a path function. 

Internal energy is a state function because the value depends only on the current state of the system and not on the path taken or process undergone to prepare it. 

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