The work done (WA B) by the gas, if 5 moles of an ideal gas...

The work done $\left(W_{A B}\right)$ by the gas, if 5 moles of an ideal gas is carried by a quasi state isothermal process at $500 \mathrm{~K}$ to twice its volume, is:
(a) $1500 \mathrm{~J}$
(b) $14407 \mathrm{~J}$
(c) $13380 \mathrm{~J}$
(d) $14890 \mathrm{~J}$

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Key Concepts

Calculation of Work in an Isothermal Process

In an isothermal expansion or compression, the work done by or on the gas is determined by integrating the pressure with respect to volume, leading to the formula W = nRT ln(V_final/V_initial). This expression is central in thermodynamics for computing energy changes in processes where the temperature remains fixed.

Ideal Gas Law

The ideal gas law (PV = nRT) relates the pressure, volume, and temperature of an ideal gas with the number of moles and the universal gas constant. It is fundamental to understanding the behavior of gases under various conditions and serves as the basis for deriving thermodynamic relationships during different processes.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout the change in volume and pressure. This results in the maintenance of the product PV as a constant and simplifies the analysis of the gas behavior using the ideal gas law, particularly in deriving work calculations.

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