<h3> Boyle's Law </h3>

Robert Boyle experimented with the effect of pressure on gas volume while temperature is constant. He published the result of his research based on that experiment in 1660; that is known as Boyle's Law. The law is:

At constant temperature, the volume of a certain mass of a gas is inversely proportional to the pressure applied to it.

If at constant temperature T, the gas volume is V and the pressure applied to it is P; then according to Boyle's Law,

$$⇒ V∝{1\over P}; $$  [while T is constant]
$$ ∴ V = {C{ 1\over P}}$$   [here C is proportional constant]
$$ ∴ PV = C..........(i) $$

-image author 정회민 from wiki-commons

Therefore, at constant temperature (T), the product of gas volume (V) and applied pressure (P) is constant. That means, with constant temperature, if another pressure (P1) is applied to the same gas and the gas volume becomes V1; then,

$$ P_1V_1 = C..........(ii)$$
similarly,$$ P_2V_2 = P_3V_3 =......P_nV_n = K $$
$$ ∴ P_nV_n= C..........(iii) $$

According to Boyle's Law,

$$ C = PV = Pressure \times Volume $$
$$ = {Force \over Area} \times Area \times Height $$
$$ = Force \times Displacement $$
$$ = Work $$

So we can say, at constant temperature, the pressure-volume work of a gas with a certain mass is equal to the proportional constant C of Boyle's Law. In SI system, the unit of C is Joule.

$$ C = PV $$
$$= Pressure \times Volume $$    $$ [P={N \over m^2}]$$
$$ = {N \over m^2} \times m^3 = Nm $$
$$ = J $$

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