Question:1.  Deduce the combined law of Charles & Boyle’s law.

Or, Find out the relationship among temperature, pressure & volume of gases

Or, Show that, the product of pressure and volume is directly proportional to the absolute temp.

Ans.: According to Boyle’s law: “At constant temperature, the volume of a definite mass of a given gas is inversely proportional to the pressure exerted on it.”

According to Charles’ law: “At constant pressure, the volume of a definite mass of a given gas is directly proportional to the absolute temperature.

Combining above two laws, (equations i & ii) –

That is, the product of pressure & volume of a fixed mass of gas is directly proportional to its absolute temperature. This is called the combined law of Charles’ & Bovle’s

Question:2.  Deduce combined law of Boyle’s, Charles’ & Avogadro’s law.

Or, Deduce ideal gas equation. Or, Show that PV = nRT.

Ans.:  According to Boyle’s law: “At constant temp., the volume of a definite mass of a given gas is inversely proportional to the pressure exerted on the gas.”

According to Charles’ law: At constant pressure, the volume of a definite mass of a given gas is directly proportional to its absolute temperature.”

According to Avogadro’s law: Amadeo Avogadro put a relationship between volume of a gas to the number of molecules at constant temperature and pressure. This has now been accepted as a law and is known as Avogadro’s law. The law states that, “Equal volumes of all gases, under similar conditions of temperature and pressure contain equal number of molecules”. Then, from Avogadro’s law one can write,

Combining above three laws, (equations i, ii  & iii) –

Where R is a constant of proportionality and is known as universal gas constant. The value of R is same for all gases. However, the numerical value of R varies with the units in which pressure, volume and temp. are expressed. Finally we can express above equation as

PV = nRT.

The above equation (4) is called ideal gas equation.

So, the product of the volume of a given gas and the pressure exerted on it, is equal to the product of mole number of gas, molar gas constant & absolute temperature.

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