State the first law of thermodynamics for isochoric process.


Isochoric process

The isochoric process is a thermodynamic process that takes place at a constant volume. It’s also known as a constant-volume process or an isometric process. The term isochoric comes from the Greek words ‘iso’, which means ‘constant’, and ‘choric’, which implies ‘space’ or ‘volume’. An isochoric process is one for which,

Vf = Vi (Δv = 0, dv = 0)

First law of thermodynamics

The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed. It can, however, be transferred from one location to another and converted to and from other forms of energy.

The equation for the first law of thermodynamics is given as;

ΔU = q + W


  • ΔU = change in internal energy of the system.
  • q = algebraic sum of heat transfer between system and surroundings.
  • W = work interaction of the system with its surroundings.

First law of thermodynamics for isochoric process

The work done in an isochoric process is zero. Hence from the first law of thermodynamics, since

dW = P dV = 0 when V = constant.

dQ = dU (isochoric process)

The total heat supplied or rejected is also equal to the increase or decrease in the internal energy of the system.

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