11.13. POINTS TO PONDER

1. Temperature of a body is related to its average internal energy, not to the kinetic energy of motion of its centre of mass. A bullet fired from a gun is not at a higher temperature because of its high speed.

This point highlights that the concept of temperature is fundamentally linked to the internal energy of a substance. Internal energy is the total kinetic and potential energy of the molecules within a substance. The temperature reflects the average energy of these molecules. When a bullet is fired, although it is moving quickly (and we might intuitively think its kinetic energy makes it 'hotter'), its temperature is determined by the energy levels of its molecules, which does not increase due to motion alone.

Think of a pot of water on a stove. When the stove heats the pot, the water's internal energy increases due to the kinetic energy of water molecules moving rapidly. If you were to throw a pebble into that pot, the pebble might move fast, but it doesn't increase the water's temperature—it's the heating element that raises the water's temperature by increasing the internal energy of the molecules, not external motion.

2. Equilibrium in thermodynamics refers to the situation when macroscopic variables describing the thermodynamic state of a system do not depend on time. Equilibrium of a system in mechanics means the net external force and torque on the system are zero.

In thermodynamics, equilibrium is defined as a state where properties like temperature, pressure, and volume remain constant over time. For instance, if a gas is contained in a sealed, insulated box and its temperature doesn't change, the system is in thermodynamic equilibrium. In contrast, in mechanics, equilibrium means that objects are at rest, or if in motion, they maintain constant velocity, resulting from balanced forces and torques.

Imagine a car at rest on a flat road—it's in mechanical equilibrium because the forces acting on it (gravity and friction) sum to zero. Now think of a sealed bottle of soda. If it stays in your refrigerator for hours without changing in temperature, it is in thermodynamic equilibrium, even if its contents keep moving slightly because of carbon dioxide bubbles.

3. In a state of thermodynamic equilibrium, the microscopic constituents of a system are not in equilibrium (in the sense of mechanics).

This point clarifies that while a system might be in thermodynamic equilibrium (stable macroscopic properties), the individual molecules or particles within that system are still constantly moving and interacting with each other. For example, even if the temperature of a container of gas remains the same, the gas molecules are in constant motion, colliding and bouncing off each other, which illustrates that microscopic behavior does not necessarily reflect macroscopic stability.

Think about a calm lake. While the surface of the water appears still and flat (indicating equilibrium), beneath that surface, the water molecules are jostling around due to thermal energy. Similarly, people sitting quietly in a room may look calm, but they are constantly breathing and slightly shifting their positions, reflecting the constant motion at a microscopic level.

4. Heat capacity, in general, depends on the process the system goes through when heat is supplied.

Heat capacity is a measure of how much heat energy is required to change the temperature of a substance by a certain amount. It varies depending on the process (constant pressure or constant volume) because different conditions allow for different behaviors in how heat is absorbed or released. For instance, heating a gas in a rigid container (constant volume) affects its internal energy differently than heating it in a flexible container (constant pressure).

Consider cooking food. If you heat a pot of water with the lid on (constant volume), it takes longer to boil because the steam can't escape, trapping energy inside. If you cook with the lid off (constant pressure), it might boil faster as steam escapes, showing how both processes change heat absorption and temperature change.

5. In isothermal quasi-static processes, heat is absorbed or given out by the system even though at every stage the gas has the same temperature as that of the surrounding reservoir. This is possible because of the infinitesimal difference in temperature between the system and the reservoir.

Isothermal processes are characterized by constant temperature. Even as heat flows into or out of a system to keep the temperature steady, the system can absorb or release energy. This is explained by the notion that the temperature difference is very small, allowing heat transfer despite the temperature remaining constant. Thus, a gas might expand while absorbing heat, yet its temperature doesn't rise, due to gradual balance with the surroundings.

Think of a sponge soaked in water. If the sponge is placed on a table where the surrounding air is a bit cooler than the sponge, it will slowly release moisture into the air, maintaining a steady moisture content (analogous to temperature), yet it continually transfers heat energy (moisture) to the air. The sponge remains humid without getting drier instantly because this transfer happens gradually.

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