Question

USE MATHEMATICAL AND COMPUTATIONAL THINKING TO DETERMINE THE MISSING PRESSURE, TEMPERATURE, OR VOLUME. (BOYLE’S LAW AND CHARLES’S LAW)


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Answer 1

Answer:

Boyle's law:

➛ It states that, volume of a given mass of a dry gas is inversely proportional to its pressure at constant temperature.

Mathematical expression of Boyle's law:

Suppose gas occupies volume V₁ when its pressure is P₁; then

➥ V₁ ∝ 1/P₁

➥ V₁ = k/P₁

➥ P₁V₁ = k = constant

If V₂ is the volume occupied when the pressure P₂ is at the same temperature; then

➥ V₂ ∝ 1/P₂

➥ V₂ = k/P₂

➥ P₂V₂ = k = constant

∴ P₁V₁ = P₂V₂ = k; [ at a constant temperature ]

This is called Boyle's law equation.

Charles' law:

➛ It states that, volume of a given mass of a dry gas is directly proportional to its absolute ( kelvin ) temperature if the pressure remains constant.

Mathematical expression of Charles' law:

Suppose gas occupies volume V₁ cm³ at T₁ temperature and V₂ cm³ at T₂ temperature, then by Charles' law,

➥ V₁ ∝ T₁

➥ V₁ = kT₁ [ k is constant ]

➥ V₁/T₁ = k

and, (second case)

➥ V₂ ∝ T₂

➥ V₂ = kT₂

➥ V₂/T₂ = k

∴ V₁/T₁ = V₂/T₂ = k [ if pressure is constant ]

This is called Charles' law equation.

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