The general law of expansion or compression of a perfect gas is:
![](data:image/png;base64,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)
It gives the relationship between pressure and volume of a given quantity of gas. The value of n depends upon the nature of gas, and condition under which the changes (i.e. expansion or compression) takes place. The value of n may be between zero and infinity. But the following values of n are important from the subject point of view:
It gives the relationship between pressure and volume of a given quantity of gas. The value of n depends upon the nature of gas, and condition under which the changes (i.e. expansion or compression) takes place. The value of n may be between zero and infinity. But the following values of n are important from the subject point of view:
1. When n = 0, then pv° = Constant, i.e. p = Constant. In other words, for the expansion or compression of a perfect gas at constant pressure, n= 0.
2. When n = 1, then pv = Constant, i.e. the expansion or compression is isothermal or hyperbolic.
3. When n lies between 1 and n, the expansion or compression is polytropic, i.e.
![](data:image/png;base64,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)
4. When n = Æ”, the expansion or compression is adiabatic, i.e.
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5. When n = ∞, the expansion or compression is at constant volume, i.e. v = Constant.
Fig 5.5 shows the curves of expansion of a perfect gas for different values of n. We see that greater the value of n, steeper is the curve of expansion.
2. When n = 1, then pv = Constant, i.e. the expansion or compression is isothermal or hyperbolic.
3. When n lies between 1 and n, the expansion or compression is polytropic, i.e.
4. When n = Æ”, the expansion or compression is adiabatic, i.e.
5. When n = ∞, the expansion or compression is at constant volume, i.e. v = Constant.
Fig 5.5 shows the curves of expansion of a perfect gas for different values of n. We see that greater the value of n, steeper is the curve of expansion.
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