The Volume of an ideal gas is 1 liter column and its...

The Volume of an ideal gas is 1 liter column and its Pressure is equal to $72 \mathrm{~cm}$ of $\mathrm{Hg}$. The Volume of gas is made 900 $\mathrm{cm}^{3}$ by compressing it isothermally. The stress of the gas will be $\ldots \ldots \ldots \ldots .$ Hg column. (A) $4 \mathrm{~cm}$ (B) $6 \mathrm{~cm}$ (C) $7 \mathrm{~cm}$ (D) $8 \mathrm{~cm}$

The Volume of an ideal gas is 1 liter column and its Pressure is equal to $72 \mathrm{~cm}$ of $\mathrm{Hg}$. The Volume of gas is made 900 $\mathrm{cm}^{3}$ by compressing it isothermally. The stress of the gas will be $\ldots \ldots \ldots \ldots .$ Hg column.
(A) $4 \mathrm{~cm}$
(B) $6 \mathrm{~cm}$
(C) $7 \mathrm{~cm}$
(D) $8 \mathrm{~cm}$

Key Concepts

Unit Conversion in Gas Laws

Accurate unit conversion is essential when applying gas laws to real-world scenarios to ensure that all quantities are in a consistent set of units. This often involves converting measurements such as liters to cubic centimeters or determining the equivalence of pressure units, such as the height of a mercury column, to the standard units used in gas law equations. Proper conversions ensure that calculations based on Boyle’s Law or the Ideal Gas Law yield correct and meaningful results.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation relating the pressure, volume, temperature, and amount of an ideal gas. Although the full equation is PV = nRT, when temperature and the amount of gas are held constant, it simplifies to Boyle's Law. This concept helps in understanding how changing one state variable (like volume) affects another (like pressure) under constant-temperature conditions.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout. In the context of an ideal gas, this implies that any change in the volume of the gas must be balanced by an inverse change in its pressure, according to Boyle's Law. Since the temperature is constant, the internal energy of an ideal gas does not change during the process.

Boyle's Law

Boyle's Law states that for a fixed quantity of an ideal gas kept at constant temperature, the pressure and volume are inversely proportional. This means that if the volume of the gas decreases, its pressure increases such that the product of pressure and volume remains constant. This principle is crucial when analyzing processes where the temperature remains unchanged, as it allows one to calculate the new pressure after a change in volume.

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