An ideal gas is heated at constant pressure and absorbs...

An ideal gas is heated at constant pressure and absorbs amount of heat $Q$. If the adiabatic exponent is $\gamma$ then the fraction of heat absorbed in raising the internal energy and performing the work, is (a) $1-\frac{1}{\gamma}$ (b) $1+\frac{1}{\gamma}$ (c) $1-\frac{2}{\gamma}$ (d) $1+\frac{2}{\gamma}$

An ideal gas is heated at constant pressure and absorbs amount of heat $Q$. If the adiabatic exponent is $\gamma$ then the fraction of heat absorbed in raising the internal energy and performing the work, is
(a) $1-\frac{1}{\gamma}$
(b) $1+\frac{1}{\gamma}$
(c) $1-\frac{2}{\gamma}$
(d) $1+\frac{2}{\gamma}$

Key Concepts

Ideal Gas

An ideal gas is a theoretical model in which the particles are assumed to have no volume and do not interact except through elastic collisions. This simplifies the analysis of thermodynamic processes as it allows direct application of the ideal gas law relating pressure, volume, and temperature.

Isobaric (Constant Pressure) Process

An isobaric process is one in which the pressure remains constant throughout. For an ideal gas undergoing this process, the heat added results in both a change in internal energy and work done by the gas due to expansion, with the heat capacity at constant pressure (Cp) being used to quantify the energy required per unit temperature change.

First Law of Thermodynamics

The first law of thermodynamics states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system. In an isobaric process, this principle is applied by dividing the absorbed heat between increasing the internal energy and performing work during expansion.

Specific Heats and Adiabatic Exponent

The specific heats at constant volume (Cv) and constant pressure (Cp) are intrinsic properties of a substance, with their difference being equal to the gas constant (R) for an ideal gas. The adiabatic exponent (?) is defined as the ratio Cp/Cv, and it plays a critical role in determining the fraction of heat used to change a gas's internal energy (nCv?T) relative to the total heat added (nCp?T) in processes such as isobaric heating.

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