Which of the following is /are true about the isothermal...

Which of the following is /are true about the isothermal expansion of an ideal gas?
(a) $\Delta \mathrm{U}=0$
(b) $\Delta \mathrm{T}=0$
(c) $\mathrm{q}=2.303 \mathrm{nRT} \log _{10}\left(\frac{\mathrm{v}_1}{\mathrm{v}_2}\right)$
(d) $\mathrm{q}=0$

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 any work done by or on the system is exactly balanced by heat transfer, ensuring that the internal energy, which depends solely on temperature for an ideal gas, remains unchanged.

Internal Energy in an Ideal Gas

In an ideal gas, the internal energy is a function solely of its temperature. This means that during any process where the temperature remains constant — such as in an isothermal process — the change in internal energy (?U) is zero regardless of volume or pressure changes.

Heat Transfer in Isothermal Processes

During an isothermal process for an ideal gas, even though the internal energy change is zero, heat transfer occurs to compensate for the work done by or on the system. This heat transfer is equal in magnitude (but opposite in sign) to the work done, ensuring that the temperature remains constant throughout the process.

Logarithmic Relationship in Isothermal Expansion

The work done (and thus the heat transferred) during an isothermal expansion of an ideal gas can be expressed using a logarithmic relationship. Specifically, it is given by the equation q = nRT ln(V_final/V_initial). This equation can also be written in terms of the common logarithm as q = 2.303 nRT log10(V_final/V_initial), showing the mathematical relationship between volume changes and heat/work in the process.

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