One mole of oxygen is heated at constant pressure starting at 0^∘ C. How much heat energy in cal

step 1 Hello students, in the question it is given that one mole of oxygen is heated at constant pressu

One mole of oxygen is heated at constant pressure starting...

One mole of oxygen is heated at constant pressure starting at $0^{\circ} \mathrm{C}$. How much heat energy in cal must be added to the gas to double its volume ? Take $\mathrm{R}=2\{(\mathrm{cal}) /($ mole $)\}$
(A) 1938
(B) 1920
(C) 1911
(D) 1957

Key Concepts

Heat Capacities (Cp and Cv)

Heat capacity at constant pressure (Cp) and constant volume (Cv) are measures of the energy required to raise the temperature of the gas under different conditions. For an ideal gas, the relation Cp = Cv + R holds, where R is the gas constant. This concept is essential in determining the total heat added during a process, as it connects the energy needed to increase the internal energy and perform work during expansion.

First Law of Thermodynamics

The first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added minus the work done by the system (?U = Q - W), provides the framework for energy conservation in thermodynamic processes. In an isobaric process, this law is used to relate the heat energy added to the gas to both the increase in internal energy and the work done during expansion.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, is fundamental for relating the pressure, volume, and temperature of an ideal gas. It allows us to deduce how one variable changes when another is held constant; for instance, at constant pressure, volume is directly proportional to temperature. This relation is key to determining the change in temperature when the volume of the gas is doubled.

Isobaric Process

An isobaric process is one in which the pressure remains constant while other state variables such as volume and temperature change. In such processes, the work done by the gas and the heat added are directly related to the change in temperature, making it possible to apply specific heat capacities to calculate energy exchanges.

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