One mole of O2 gas having a Volume equal to 22.4 liter at O c and 1 atmospheric Pressure is Comp

step 1 Hello in the question it is given that one mole of oxygen gas having a volume equal to 20 to 4 l

One mole of O2 gas having a Volume equal to 22.4 liter at O...

One mole of $\mathrm{O}_{2}$ gas having a Volume equal to $22.4$ liter at $\mathrm{O}$ $c$ and 1 atmospheric Pressure is Compressed isothermally so that its volume reduces to $11.2$ liters. The work done in this Process is (A) $1672.4 \mathrm{~J}$ (B) $-1728 \mathrm{~J}$ (C) $1728 \mathrm{~J}$ (D) $-1572.4 \mathrm{~J}$

One mole of $\mathrm{O}_{2}$ gas having a Volume equal to $22.4$ liter at $\mathrm{O}$ $c$ and 1 atmospheric Pressure is Compressed isothermally so that its volume reduces to $11.2$ liters. The work done in this Process is
(A) $1672.4 \mathrm{~J}$ (B) $-1728 \mathrm{~J}$
(C) $1728 \mathrm{~J}$
(D) $-1572.4 \mathrm{~J}$

Key Concepts

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout the process. For an ideal gas, this implies that there is no change in internal energy during the process, and any work done by or on the system is compensated by heat exchange with the surroundings. This concept is fundamental in thermodynamics and is commonly applied in the analysis of processes in heat engines and refrigerators.

Work Done in a Reversible Isothermal Process

In a reversible isothermal process involving an ideal gas, the work done is calculated using the formula W = nRT ln(V_final/V_initial), where n is the number of moles, R is the gas constant, T is the constant temperature, and V_final and V_initial are the final and initial volumes, respectively. The logarithmic nature of the formula arises from integrating the pressure with respect to volume when the pressure is defined by the ideal gas law, and the sign of the work indicates whether work is done on or by the system.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure, volume, and temperature of an ideal gas. This law provides the necessary link to calculate various thermodynamic quantities in processes involving gases, and it is particularly important in isothermal processes where maintaining a constant temperature allows for straightforward substitution into other formulas, such as the work calculation for reversible processes.

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