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Question
Explain in detail the isochoric process.
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Solution
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 the pressure axis as shown in Figure.
Isochoric process with increased pressure
Isochoric process with decreased pressure
Isochoric process
P = `((μ"R")/"V")"T"` ...............(1)
where `((μ"R")/"V")` = constant
We can infer that the pressure is directly proportional to temperature. This implies that the P-T graph for an isochoric process is a straight line passing through the origin. If gas goes from the state (Pi, Ti) to (Pf, Tf) at constant volume, then the system satisfies the following equation
`"P"_"i"/"T"_"i" = "P"_"f"/"T"_"f"` .....,,,(2)
For an isochoric processes, ∆V = 0 and W = 0. Then the first law becomes
∆U = 0 .................(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.
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