This is the fractional change of volume as pressure is changed at constant temperature for a gas.

This is the fractional change of volume as pressure is changed at constant temperature for a gas.

• A. Coefficient of isothermal compressibility
• B. Thermal expansion coefficient
• C. Adiabatic index
• D. Gas constant

Answer: (A)

Isothermal compressibility describes how easily a gas’s volume changes when pressure is altered at a fixed temperature. It’s defined as κ_T = −(1/V) (∂V/∂P)_T, with the minus sign ensuring the measure is positive when pressure increases and volume decreases. This directly matches the prompt’s idea of a fractional volume change per unit pressure change at constant temperature. For an ideal gas, V = nRT/P. Differentiating at constant T gives ∂V/∂P|_T = −nRT/P^2. Substituting into the definition yields κ_T = −(1/V)(−nRT/P^2) = (nRT/P^2)/(nRT/P) = 1/P. So the isothermal compressibility is 1 over pressure in the ideal-gas limit, illustrating how volume responds to pressure under isothermal conditions. Other options describe different properties: the thermal expansion coefficient relates to how volume changes with temperature at constant pressure, the adiabatic index is Cp/Cv describing energy changes during rapid compression/expansion, and the gas constant is a fundamental constant related to both gas behavior and units.

Isothermal compressibility describes how easily a gas’s volume changes when pressure is altered at a fixed temperature. It’s defined as κ_T = −(1/V) (∂V/∂P)_T, with the minus sign ensuring the measure is positive when pressure increases and volume decreases. This directly matches the prompt’s idea of a fractional volume change per unit pressure change at constant temperature.

For an ideal gas, V = nRT/P. Differentiating at constant T gives ∂V/∂P|_T = −nRT/P^2. Substituting into the definition yields κ_T = −(1/V)(−nRT/P^2) = (nRT/P^2)/(nRT/P) = 1/P. So the isothermal compressibility is 1 over pressure in the ideal-gas limit, illustrating how volume responds to pressure under isothermal conditions.

Other options describe different properties: the thermal expansion coefficient relates to how volume changes with temperature at constant pressure, the adiabatic index is Cp/Cv describing energy changes during rapid compression/expansion, and the gas constant is a fundamental constant related to both gas behavior and units.