Matter Revision Notes

What is Gas Pressure?

Gas pressure is caused by gas particles colliding with the walls of their container. Each collision exerts a tiny force, and the sum of all these forces over a given area creates the measurable pressure. The force exerted by gas particles on a surface always acts at a right angle (perpendicular) to that surface. This is why a balloon inflates evenly – the gas pushes outwards in all directions, perpendicular to the curved surface.

Compressibility and Expansibility of Gases

Unlike solids and liquids, gases have large spaces between their particles, making them highly compressible. This means that if you apply an external force, you can reduce the volume a gas occupies. Conversely, gases can also be easily expanded by reducing the external pressure or increasing the volume of the container. This characteristic is unique to gases and is vital for many industrial and domestic applications.

Pressure Changes and Volume

When a gas is compressed, its volume decreases. With the same number of particles in a smaller space, the particles collide with the container walls more frequently, leading to an increase in pressure. The opposite happens during expansion: as volume increases, particles collide less frequently with the walls, causing the pressure to decrease. This inverse relationship between pressure and volume (at constant temperature) is an important concept in gas behaviour.

PAG: Investigating Pressure Changes in Gases

A practical investigation (PAG) to demonstrate gas compressibility often involves a syringe. You can seal the end of a syringe, then push the plunger in. This reduces the volume of the trapped air, and you will feel increased resistance, indicating higher pressure. Conversely, pulling the plunger out (if the seal is imperfect, or using another method to expand) would decrease the pressure. Safety points include ensuring the syringe is clean and avoiding pointing it at others.

Atomic Structure Overview

An atom is the smallest unit of an element that retains the chemical properties of that element. It is composed of a central, positively charged nucleus and negatively charged electrons orbiting or existing in an 'electron cloud' around this nucleus. The atom as a whole is electrically neutral, meaning the total positive charge of the nucleus balances the total negative charge of the electrons.

The Nucleus: The Atom's Core

The nucleus is located at the very centre of the atom. It carries a net positive charge due to the protons it contains. Crucially, the nucleus is incredibly dense and accounts for almost all of the atom's mass, typically over 99.9%. Despite holding nearly all the mass, the nuclear radius is vastly smaller than the atomic radius. For instance, the nuclear radius is roughly 100,000 times smaller than the atomic radius.

Electrons and Atomic Size

Electrons are negatively charged particles that surround the nucleus. They orbit in shells or energy levels, and their distribution defines the overall size and volume of the atom. Despite occupying the vast majority of the atom's volume, electrons have very little mass compared to the nucleus. Their negative charge balances the positive charge of the protons in the nucleus, making the atom electrically neutral in its ground state.

Mass and Charge Distribution

To summarise the key features: the nucleus is positively charged and contains almost all of the atom's mass in a very small volume. The electrons are negatively charged, have negligible mass, and determine the overall size of the atom. The positive charge of the nucleus is balanced by the total negative charge of the electrons, resulting in a neutral atom.

Factors Affecting Pressure in Liquids

Pressure in a liquid is directly proportional to three factors: depth (h), density of the liquid (ρ), and acceleration due to gravity (g). The formula for calculating pressure at a certain depth in a liquid is P = hρg. This means that as any of these values increase, the pressure at that point will also increase. For instance, a swimmer diving deeper into the ocean experiences higher pressure due to the increased height of the water column above them. Similarly, being in a denser liquid like mercury would lead to much higher pressures at the same depth compared to water, because mercury has a greater mass per unit volume.

Understanding Upthrust (Higher)

Upthrust, also known as buoyancy, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. This force arises directly from the pressure difference within the fluid. As established, pressure in a fluid increases with depth. Therefore, the pressure on the bottom surface of a submerged object is greater than the pressure on its top surface, because the bottom surface is at a greater depth. This differential pressure results in a net upward force, which is the upthrust. The horizontal pressures acting on the sides of the object cancel each other out.

Origin of Upthrust from Pressure Difference (Higher)

Imagine a submerged cube. The liquid exerts a force on all its surfaces. The downward force on the top surface is F_top = P_top × A, where P_top = h_topρg. The upward force on the bottom surface is F_bottom = P_bottom × A, where P_bottom = h_bottomρg. Since h_bottom > h_top, it follows that P_bottom > P_top, and thus F_bottom > F_top. The net upward force, upthrust, is F_bottom - F_top = (h_bottomρgA) - (h_topρgA) = (h_bottom - h_top)ρgA. The term (h_bottom - h_top) represents the height of the object, so (h_bottom - h_top)A equals the volume of the object (or the volume of fluid displaced if partially submerged). Therefore, the upthrust equals the volume of displaced fluid multiplied by density and gravity, which is simply the weight of the displaced fluid. This illustrates Archimedes' principle.

The Formula for Internal Energy Change

The change in internal energy (or heat energy, Q) of a material is directly proportional to its mass (m), its specific heat capacity (c), and the change in its temperature (ΔT). The formula is: Q = m × c × ΔT.

'Q' represents the change in internal energy, measured in Joules (J). 'm' represents the mass of the substance, measured in kilograms (kg). 'c' represents the specific heat capacity of the substance, measured in Joules per kilogram per degree Celsius (J/kg°C). 'ΔT' represents the change in temperature, measured in degrees Celsius (°C). It is calculated as final temperature - initial temperature.

Understanding Specific Heat Capacity (c)

Specific heat capacity 'c' is a crucial property that tells us how much energy is needed to change the temperature of a specific amount of a substance. A high specific heat capacity means a substance requires a large amount of energy to increase its temperature, and it also releases a large amount of energy when its temperature decreases. Water, for instance, has a very high specific heat capacity (approximately 4200 J/kg°C), which is why it warms up slowly but also cools down slowly. Materials like metals often have lower specific heat capacities. This value is unique for each substance and must be provided or calculated from experimental data.

Applying the Formula in Calculations

To use the formula Q = m × c × ΔT, ensure all units are consistent. Mass must be in kilograms, specific heat capacity in J/kg°C, and temperature change in °C. If mass is given in grams, convert it to kilograms by dividing by 1000. The temperature change (ΔT) is always the final temperature minus the initial temperature. If the temperature decreases, ΔT will be negative, and consequently, Q will also be negative, indicating energy has been lost from the material. If the temperature increases, ΔT will be positive, and Q will be positive, indicating energy has been gained by the material.

Rearranging the Formula

The formula Q = m × c × ΔT can be rearranged to find any of the variables if the others are known.

To find mass (m): m = Q / (c × ΔT) To find specific heat capacity (c): c = Q / (m × ΔT) To find temperature change (ΔT): ΔT = Q / (m × c)

These rearrangements are useful when calculating an unknown quantity from given experimental results or problem data. Always remember to check units and convert if necessary before performing calculations.