Explain in detail the isochoric process.

Explanation

Isochoric process: This is a thermodynamic process in which the volume of the system is kept constant. But pressure, temperature and internal energy continue to be variables.
The pressure - volume graph for an isochoric process is a vertical line parallel to pressure axis as shown in Figure.

The equation of state for an isochoric process is given by
`P=((muR)/(V))T" ....(1)"`
`"where "((mmuR)/(V))="constant "`

We can infer that the pressure is direcly proportional is temperature. This implies that the `P-T` graph for an isochoric process is a straight line passing through origin.
If a gas goes from state `(P_(i),T_(i))" to "(P_(f),T_(f))` at constant volume, then the system satisfies the following volume, then the system satisfies the following equation
`(P_(i))/(T_(i))=(P_(f))/(T_(f))" ...(2)"`
For an isochoric processes, `DeltaV = 0` and `W = 0`. Then the first law becomes
`DeltaU = Q" ...(3)"`
Implying that the heat supplied is used to increase only the internal energy. As a result the temperature increases and pressure also increases.
Suppose a system loses heat to the surroundings through conducting walls by keeping the volume constant, then its internal energy decreases. As a result the temperature decreases, the pressure also decreases.