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Ideal Gas derivation.

The ideal gas equation is formulated as: PV = nRT. In this equation, P refers to the pressure of the ideal gas, V is the volume of the ideal gas, n is the total amount of ideal gas that is measured in terms of moles, R is the universal gas constant, and T is the temperature.

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According to Boyle's Law,

At constant temperature( $T)$ and number of moles of $\operatorname{gas}(\mathrm{n})$, the volume $(V)$ bears an inverse relation with the pressure(P) exerted by a gas. $$ V \propto \frac{1}{P}\ldots \ldots \ldots \ldots \ldots \ldots \ldots(1) $$

According to Charles's Law,

When pressure(P) exerted by the gas and number of moles of gas $(n)$ are constant, then volume $(V)$ of gas bears a direct relation with Temperature.

$$\mathbf{V} \propto \mathrm{T}\ldots \ldots \ldots \ldots \ldots \ldots \ldots(2)$$

According to Avogadro's Law,

When temeprature $(T)$ and pressure $(P)$ exerted by the gas are constant, then volume of gas bears a direct relation with number of moles of gas(n).

$$\mathbf{V} \propto \mathbf{n}\ldots \ldots \ldots \ldots \ldots \ldots \ldots(3)$$

Combining equation (1) (2) & (3)

$$V \propto n T / p$$

Ideal Gas Equation → P V= nRT....(R is Universal gas constant =8.314)

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