Thermodynamics

The properties of expansion and contraction of materials due to temperature changes are used in various applications in daily life. Here are a few examples:

• Bimetallic Strips in Thermostats:

  Bimetallic strips, made of two different metals with different coefficients of thermal expansion, are used in thermostats. When the temperature changes, the two metals expand or contract at different rates, causing the strip to bend. This bending is used to control a switch that turns heating or cooling systems on or off.

• Expansion Joints in Bridges and Roads:

  Bridges and roads are built with expansion joints to accommodate the expansion and contraction of the materials due to temperature changes. These joints prevent the structures from cracking or buckling under stress.

• Tightening Jar Lids:

  When a jar lid is stuck, running it under hot water can help loosen it. The heat causes the metal lid to expand slightly, making it easier to twist open.

• Hot Air Balloons:

  Hot air balloons use the principle of thermal expansion to achieve lift. Heating the air inside the balloon causes it to expand, decreasing its density compared to the surrounding air, which creates buoyancy.

• Thermometers:

  Traditional liquid-in-glass thermometers use the expansion and contraction of a liquid (like mercury or alcohol) to measure temperature. As the temperature rises, the liquid expands and rises in the tube, indicating the temperature on a scale.

Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure at constant temperature and number of moles, can be explained using the kinetic theory of gases. The kinetic theory makes the following assumptions:

• Gases consist of a large number of particles (atoms or molecules) that are in continuous, random motion.
• The volume of the particles is negligible compared to the total volume of the gas.
• The particles do not exert any attractive or repulsive forces on each other.
• Collisions between particles and the walls of the container are perfectly elastic (no energy is lost).
• The average kinetic energy of the particles is proportional to the absolute temperature of the gas.

Explanation of Boyle's Law based on Kinetic Theory:

1. Pressure and Molecular Collisions:

   Pressure exerted by a gas is due to the collisions of its particles with the walls of the container. Each collision exerts a small force on the wall. The total pressure is the sum of all these forces per unit area.

2. Changing the Volume:

   If the volume of the container is decreased while keeping the temperature constant, the particles have less space to move around in. This means they will collide with the walls more frequently.

3. Increased Collision Frequency:

   Because the particles are colliding with the walls more frequently, the force exerted on the walls per unit area (i.e., the pressure) increases.

4. Constant Kinetic Energy:

   Since the temperature is constant, the average kinetic energy of the particles remains the same. This means the average speed of the particles does not change. Therefore, each collision exerts roughly the same amount of force as before, but there are more collisions happening per unit time.

5. Inverse Relationship:

   The net effect is that decreasing the volume increases the frequency of collisions, which increases the pressure. Conversely, if the volume is increased, the particles have more space, collide with the walls less frequently, and the pressure decreases. This inverse relationship between volume and pressure at constant temperature is Boyle's Law.

In mathematical terms, Boyle's Law is expressed as: PV = k, where P is the pressure, V is the volume, and k is a constant for a given mass of gas at a constant temperature.

In summary, the kinetic theory explains Boyle's Law by linking the pressure of a gas to the frequency of collisions of its particles with the container walls. Decreasing the volume increases the collision frequency, thus increasing the pressure, and vice versa, assuming the temperature and number of particles remain constant.

More information may be found here:

• LibreTexts: Kinetic Theory of Gases
• Khan Academy: The Ideal Gas Law

Deriving the van der Waals equation of state involves modifying the ideal gas law to account for the finite size of gas molecules and the attractive forces between them. Here’s a step-by-step derivation:

1. Ideal Gas Law

   The ideal gas law is given by:

   PV = nRT

   Where:

   • P is the pressure,
   • V is the volume,
   • n is the number of moles,
   • R is the ideal gas constant,
   • T is the temperature.
2. Correction for Molecular Volume

   In an ideal gas, molecules are considered point masses. However, real gas molecules occupy a finite volume, reducing the space in which they can move. The effective volume is reduced by nb, where b is the volume excluded per mole of gas. Therefore, the corrected volume V' is:

   V' = V - nb
3. Correction for Intermolecular Forces

   Ideal gas molecules do not interact. In reality, gas molecules attract each other, reducing the pressure exerted on the container walls. This reduction in pressure is proportional to the square of the concentration (n/V). The corrected pressure P' is:

   P' = P + a(n/V)^2

   Where a is a constant that depends on the strength of the attractive forces between the molecules.

4. Van der Waals Equation

   Substitute the corrected pressure P' and corrected volume V' into the ideal gas law:

   P'V' = nRT

   Which gives:

   (P + a(n/V)^2)(V - nb) = nRT

   This is the van der Waals equation of state.

In summary, the van der Waals equation accounts for the volume occupied by gas molecules and the attractive forces between them, providing a more accurate description of real gases compared to the ideal gas law.

More information can be found on:

• LibreTexts - The van der Waals Equation of State
• FSU Chemistry - van der Waals Equation

Ferry's black body is an artificial black body designed by English physicist Horace Albert Ferry.

• A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.
• It neither reflects nor transmits any radiation and emits radiation based on its temperature, known as black-body radiation.

Ferry's black body is a closed cavity with a small hole. The inner walls are coated with a black material to absorb radiation. Radiation entering the hole undergoes multiple reflections and absorptions inside the cavity, ensuring nearly complete absorption. The small hole acts as an almost perfect black body, emitting radiation characteristic of its temperature.

Carnot's ideal heat engine is a theoretical thermodynamic cycle that provides an upper limit on the efficiency that any heat engine can achieve when operating between two heat reservoirs. It is a theoretical engine and cannot be built in practice, but it serves as a benchmark for real engines.

Here are the key aspects of Carnot's ideal heat engine:

For more detailed information, you can refer to these resources:

The kinetic theory of gases is based on the following postulates:

1. Gases are made up of a large number of molecules:

   Gases consist of a very large number of identical molecules that are perfectly elastic point masses.

2. The molecules are in constant, random motion:

   Gas molecules are in constant, random motion, moving in straight lines until they collide with each other or with the walls of the container.

3. Collisions are perfectly elastic:

   Collisions between gas molecules and between the molecules and the walls of the container are perfectly elastic. This means that no kinetic energy is lost during collisions. Source

4. The volume of the molecules is negligible:

   The volume of the gas molecules is negligible compared to the total volume of the container.

5. There are no intermolecular forces:

   There are no attractive or repulsive forces between gas molecules.

6. The average kinetic energy depends on temperature:

   The average kinetic energy of the gas molecules is directly proportional to the absolute temperature of the gas. All gases have the same kinetic energy at a specified temperature.