The work of 62.25 KJ is performed in order to compress one...

The work of $62.25 \mathrm{KJ}$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $5^{\circ} \mathrm{C}$ The gas is $\mathrm{R}=8.3\{\mathrm{~J} /(\mathrm{mole})\}$ (A) triatomic (B) diatomic (C) monoatomic (D) a mixture of monoatomic and diatomic

The work of $62.25 \mathrm{KJ}$ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $5^{\circ} \mathrm{C}$ The gas is $\mathrm{R}=8.3\{\mathrm{~J} /(\mathrm{mole})\}$
(A) triatomic
(B) diatomic
(C) monoatomic
(D) a mixture of monoatomic and diatomic

Key Concepts

First Law of Thermodynamics

The first law of thermodynamics, which states that energy cannot be created or destroyed but only transferred or transformed, underpins the analysis of work and internal energy in thermodynamic processes. In the absence of heat transfer, as in an adiabatic process, the work done on the system directly changes its internal energy.

Adiabatic Process

An adiabatic process is one in which no heat is exchanged with the surroundings. This means that all the work done on or by the system translates directly into a change in its internal energy, making it essential in analyzing temperature changes during compression or expansion without heat transfer.

Internal Energy of an Ideal Gas

For an ideal gas, the internal energy is a function of temperature alone. Changes in the internal energy, particularly during an adiabatic process, are directly tied to work done on the system, thereby providing a link between microscopic molecular motion and macroscopic thermodynamic properties.

Molar Specific Heat Capacity and Degrees of Freedom

The molar specific heat at constant volume (Cv) is related to the degrees of freedom of the molecules in a gas through the equation Cv = (f/2)R, where f represents the number of degrees of freedom and R is the gas constant. This relationship helps determine how energy is partitioned within gas molecules and is crucial for understanding the thermal behavior of different types of gases.

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