Problem 11 - A Complete Resource Book in Chemistry for JEE Main

Question

The internal energy of a substance does not depend upon (a) translational energy (b) vibrational energy (c) energy due to gravitational pull (d) rotational energy

Step-by-Step Solution

Answer

Internal energy does not depend upon energy due to gravitational pull (option c).

Step 1: Understanding Internal Energy

Internal energy is the total energy contained within a substance, accounting for molecular and atomic motion and interactions. It includes energy forms such as translational, vibrational, and rotational kinetic energy, as well as potential energy due to molecular interactions but does not include external forces.

Step 2: Identifying the Key Types of Energy in Internal Energy

Understand what each option represents: Translational energy relates to the straight-line movement of molecules, vibrational energy involves the movement within molecules, and rotational energy concerns the spinning of molecules. These are all microscopic forms of energy contributing to a substance's internal energy.

Step 3: Recognizing External Factors

Energy due to gravitational pull is not considered part of the internal energy of a substance. It is an external force affecting the substance's position in a gravitational field and doesn't directly impact the energy interactions within the substance's microscopic components.

Step 4: Conclusion

Given the options, energy due to gravitational pull is the component that internal energy does not depend upon as it deals with external, macro-level influences.

Key Concepts

Translational Energy

Translational energy refers to the motion of molecules along a straight path. It's one of the fundamental types of kinetic energy observed in a substance. Imagine molecules in a gas, freely moving in random directions. These movements can be in straight lines, making translational motion critical in determining a gas's temperature.

The kinetic energy tied to translational motion can be calculated with the formula:

• \( KE = \frac{1}{2} m v^2 \)

where \( m \) is the mass of a molecule and \( v \) is its velocity. This movement contributes significantly to a substance's internal energy, expressing how active the molecules are at any given temperature. The more molecules move, the higher the substance's temperature and internal energy.

Vibrational Energy

Vibrational energy refers to the energy due to the back-and-forth motion that occurs within molecules. This type of kinetic energy is crucial in understanding how molecules behave, especially in more complex substances like solids and liquids.

In molecules, atoms are bonded and can move around a quasi-fixed point, leading to a vibrational mode, often represented as potential energy stored during atom displacement. To quantify this, vibrational energy is often described with harmonic oscillator models:

• Vibrational modes are the specific patterns of vibration that molecules undergo.
• These contribute significantly to the internal energy, particularly at high temperatures.

The vibrational energy becomes more prominent in substances when there is more energy available for these internal movements, such as increasing temperature, directly impacting how substances store and transfer energy.

Rotational Energy

Rotational energy highlights how molecules can spin around their axis. Just like planets that spin in space, molecules rotate in different directions and planes, enhancing the complexity of their internal movements.

This physical property influences internal energy, and is best understood through the formula:

• \( KE_{rot} = \frac{1}{2} I \omega^2 \)

where \( I \) represents the moment of inertia, and \( \omega \) is the angular velocity. This characteristic of molecules is particularly evident in gases, where increased rotation can relate to greater internal energy. Much like vibrating energy, these motions are more actively studied in contexts where temperature and pressure influence their state and behavior.