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) $1-\frac{i}{\gamma}$ (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) $1-\frac{i}{\gamma}$
(b) $1+\frac{1}{\gamma}$
(c) $1-\frac{2}{\gamma}$
(d) $1+\frac{2}{\gamma}$

Key Concepts

Relationship Between Cp, Cv, and the Adiabatic Exponent (?)

For an ideal gas, the ratio of specific heats, ? (gamma), is defined as Cp/Cv. This relationship allows one to express the fraction of heat that increases internal energy and the fraction that is used for work during a constant-pressure process in terms of ?. Specifically, the fraction of the heat that goes into raising the internal energy is Cv/Cp = 1/?, and the remainder, which is used to perform work, is (Cp - Cv)/Cp = 1 - 1/?.

Constant Pressure Process for an Ideal Gas

In a constant pressure process, the gas expands as it is heated, meaning that part of the added heat is converted into work. The process is characterized by the relation Q = nCp?T, where Q is the heat absorbed, n is the number of moles, and ?T is the temperature change. This concept is essential for understanding how energy is partitioned between doing work and increasing the internal energy of the gas.

First Law of Thermodynamics

This law states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In the context of a constant-pressure process, the absorbed heat is partitioned between increasing the internal energy and doing work against the external pressure.

Specific Heat Capacities

Specific heat capacities at constant volume (Cv) and constant pressure (Cp) describe how much heat is needed to change the temperature of a substance. For an ideal gas, internal energy change depends on Cv, while the heat added at constant pressure involves Cp, which is greater than Cv because it accounts for work done during expansion.

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