Question

State the first law of thermodynamics for isochoric process.

Answer 1

Isochoric process

• The isochoric process is a thermodynamic process that takes place at a constant volume.
• It is also known as a constant-volume process or an isometric process.
• In an isochoric process, the final volume and initial volume are the same. Therefore, the change in volume is zero.
• $V_f=V_i(\Delta v=0,dv=0)$ where

$$\begin{gathered} V_f=Finalvolume \\ {V}_i=Initialvolume \\ ∆v=changeinvolume \\ dv=changeinvolume \end{gathered}$$

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.
• According to the principle of conservation of energy, energy can neither be created nor be 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;

$\Delta U=q+W$where,

$\Delta U=$ change in the internal energy of the system.

$q=$the 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 is given by $dW=Pdv$.
• Since in an isochoric process $dv=0$, therefore, the work done is also zero.
• From the first law of thermodynamics we have, $dU=dq+dW$

$$\begin{gathered} \Rightarrow dU=dq+0 \\ \Rightarrow dU=dq \end{gathered}$$

• Hence the first law of thermodynamics for an isochoric process is that the total heat supplied or rejected is also equal to the increase or decrease in the internal energy of the system.