Topic 1a: Energy Stores and Transfers Master Study Guide

Fundamentals of Energy Stores and Systems

Energy stores are a central concept in physics: energy is never used up, but is instead transferred between different stores and different objects.
There are eight primary energy stores that must be known: - Thermal Energy Stores: Also referred to as internal energy stores. - Kinetic Energy Stores: Associated with moving objects. - Gravitational Potential Energy Stores: Associated with an object's position in a gravitational field. - Elastic Potential Energy Stores: Associated with stretched or squashed objects. - Chemical Energy Stores: Associated with chemical bonds. - Magnetic Energy Stores: Associated with magnetic fields. - Electrostatic Energy Stores: Associated with electric charges. - Nuclear Energy Stores: Associated with atomic nuclei.
A system refers to a single object (e.g., air in a piston) or a group of objects (e.g., two colliding vehicles).
When a system changes, energy is transferred. Transfers can occur into or away from the system, between objects within the system, or between different types of stores.
Closed Systems: These are systems where neither matter nor energy can enter or leave. In a closed system, the net change in total energy is always zero.
Ways energy can be transferred include: - Heating: For example, in a kettle, energy is transferred electrically to the thermal energy store of the heating element, then to the water's thermal energy store by heating. - Radiation: Such as transfers via light or sound. - Mechanically/Doing Work: Work done is synonymous with energy transferred. This occurs when a current flows (against resistance) or when a force moves an object.

Work Done and Mechanical Transfers

Initial Force and Throwing: When a person throws a ball upwards, the initial force exerted does work. Energy is transferred from the chemical energy store of the person's arm to the kinetic and gravitational potential energy stores of both the ball and the arm.
Falling Objects: A ball dropped from a height is accelerated by gravity. The gravitational force does work, transferring energy from the ball's gravitational potential energy store to its kinetic energy store.
Friction and Braking: The friction between a car's brakes and its wheels does work as the car slows down. Energy is transferred from the wheels' kinetic energy stores to the thermal energy store of the surroundings.
Collisions: In a collision between a car and a stationary object, the normal contact force does work. This causes energy to be transferred from the car’s kinetic energy store to other stores, such as the thermal and elastic potential energy stores of both the car body and the object.

Kinetic, Gravitational Potential, and Elastic Energy Stores

Kinetic Energy ( $E_k$ ): Stationary objects have no kinetic energy; the store depends on mass and speed. The greater the mass and velocity, the more energy in the store. - Formula: $E_k = \frac{1}{2}mv^2$ - Units: Kinetic energy is in Joules ( $J$ ), mass is in kilograms ( $kg$ ), and speed is in meters per second ( $m/s$ ). - Example: A $2500\,kg$ car traveling at $20\,m/s$ has $E_k = 0.5 \times 2500 \times 20^2 = 500,000\,J$ .
Gravitational Potential Energy ( $E_p$ ): Lifting an object in a gravitational field requires work, transferring energy to the gravitational potential energy (g.p.e.) store. - Formula: $E_p = mgh$ - Components: mass ( $m$ ), gravitational field strength ( $g$ ), and change in height ( $h$ ). - Field Strength: $g$ is measured in $N/kg$ .
Energy Transfers in Falling Objects: When an object falls with no air resistance, the energy lost from the g.p.e. store is exactly equal to the energy gained in the kinetic energy store. - In real-world scenarios, air resistance acts against the falling object, causing some energy to dissipate into the thermal energy stores of the object and its surroundings.
Elastic Potential Energy ( $E_e$ ): Stretching or squashing a spring transfers energy to this store. - Formula: $E_e = \frac{1}{2}ke^2$ - Provided the limit of proportionality is not exceeded; where $k$ is the spring constant ( $N/m$ ) and $e$ is the extension ( $m$ ).

Specific Heat Capacity

Specific heat capacity is defined as the amount of energy required to raise the temperature of $1\,kg$ of a substance by $1^\circ\text{C}$ .
Different substances have different capacities; those that require high energy to warm up also release high energy when cooling down.
Formula: $\Delta E = mc\Delta\theta$ - $\Delta E$ : Change in thermal energy ( $J$ ). - $m$ : Mass ( $kg$ ). - $c$ : Specific heat capacity ( $J/kg^\circ\text{C}$ ). - $\Delta\theta$ : Temperature change ( $^\circ\text{C}$ ).
Investigation Procedure: 1. Use a solid block of material with two holes (for a heater and thermometer). 2. Measure the mass of the block and wrap it in insulation (e.g., newspaper). 3. Measure initial temperature and set the power supply potential difference to $10\,V$ . 4. Switch on the heater and stopwatch; take temperature and current ( $I$ ) readings every minute for 10 minutes. 5. Calculate power using $P = VI$ and energy transferred using $E = Pt$ ( $t$ in seconds). 6. Plot a graph of temperature against energy transferred. The gradient of the straight-line portion is \Delta\theta \Delta E. 7. Calculate specific heat capacity: c = 1 (\text{gradient} \times \text{mass of block}).

Conservation of Energy and Power

The Conservation of Energy Principle: Energy can be transferred usefully, stored, or dissipated, but it can never be created or destroyed.
Dissipation: When energy is transferred, not all of it is useful. Dissipated energy (often called "wasted energy") usually transfers to thermal stores. - Example: In a mobile phone, chemical energy from the battery is usefully transferred, but energy is also dissipated to the thermal stores of the phone and surroundings. - Example: In a closed system (sealed flask of soup), energy moves from hot soup to a cold spoon. No energy leaves the system, but it dissipates to the spoon's thermal store.
Power ( $P$ ): Power is the rate of energy transfer or the rate of doing work. - Unit: Watts ( $W$ ). One Watt is defined as one Joule per second ( $1\,W = 1\,J/s$ ). - Formulas: $P = \frac{E}{t}$ and $P = \frac{W}{t}$ . - A powerful machine transfers a lot of energy in a short time. For two identical cars, the one with the higher power engine will finish a race faster because it transfers energy more quickly. - Calculation example: To lift a performer requiring $11,000\,J$ of work, Motor A takes $55\,s$ ( $P = 11,000 / 55 = 200\,W$ ) and is more powerful than Motor B, which takes $300\,s$ .

Heat Transfer Mechanisms: Conduction and Convection

Conduction: Primarily occurs in solids. It is the process where vibrating particles transfer energy to neighboring particles. - Particles being heated vibrate more and collide with neighbors, sharing kinetic energy. - Thermal conductivity is a measure of how quickly energy is transferred through a material this way. High thermal conductivity indicates quick energy transfer.
Convection: Occurs only in liquids and gases. Energetic particles move away from hotter regions toward cooler regions. - Heating a region causes particles to move faster and the space between them to increase, reducing density in that region. - Warmer, less dense regions rise above cooler, denser regions. - Convection Current: A constant heat source causes particles to rise, cool at the top, and sink again, creating a repeating cycle.

Thermal Insulation and Efficiency

Insulation Methods: - Loft Insulation: Reduces convection currents in lofts. - Cavity Walls: An inner and outer wall with an air gap. The air gap reduces conduction. Filling it with foam reduces convection. - Draught Excluders: Placed around doors and windows to reduce convection. - Double Glazing: Uses an air gap between glass sheets to reduce conduction. - Wall Thickness: Thicker walls with low thermal conductivity lead to slower rates of energy transfer.
Investigating Insulation: - Measure mass and initial temperature of hot water in a container. - Seal and wait 5 minutes; measure final temperature. - Repeat by wrapping the container in different materials (foil, newspaper, bubble wrap, cotton wool) or different thicknesses. - A lower temperature difference indicates a better insulator.
Lubrication: Used to reduce friction between moving surfaces. Usually liquids like oil that flow easily between objects. This reduces dissipated energy.
Streamlining: Reduces friction from air resistance.
Efficiency Calculations: - No device is $100\%$ efficient, except for electric heaters (where the "wasted" thermal energy is actually the useful output). - Formula 1: $\text{Efficiency} = \frac{\text{Useful output energy transfer}}{\text{Total input energy transfer}}$ - Formula 2: $\text{Efficiency} = \frac{\text{Useful power output}}{\text{Total power input}}$ - Efficiency can be expressed as a decimal or a percentage (e.g., $0.75$ or $75\%$ ).

Questions & Discussion

Q1: Describe the energy transfers that occur when the wind causes a windmill to spin. - Answer: The wind has energy in its kinetic energy store. As it hits the blades, energy is transferred mechanically to the kinetic energy store of the windmill blades.
Q1: A 2.0 kg object is dropped from a height of 10 m. Calculate the speed after it has fallen 5.0 m (g = 9.8 N/kg, no air resistance). - Step 1: Calculate GPE lost after 5m: $E_p = mgh = 2.0 \times 9.8 \times 5 = 98\,J$ . - Step 2: Since GPE lost = KE gained, $98 = \frac{1}{2}mv^2$ . - Step 3: $98 = 0.5 \times 2 \times v^2 \rightarrow 98 = v^2 \rightarrow v = \sqrt{98} \approx 9.9\,m/s$ .
Q1: Find the final temperature of 5 kg of water (initial 5 C) after 50 kJ of energy is transferred. SHC of water is 4200 J/kg C. - Step 1: convert energy to Joules: $50,000\,J$ . - Step 2: \Delta\theta = \frac{\Delta E}{mc} = \frac{50,000}{5 \times 4200} = \frac{50,000}{21,000} 2.38^\circ\text{C}. - Step 3: Final temperature = $5 + 2.38 = 7.38^\circ\text{C}$ .
Q1: A motor transfers 4.8 kJ of energy in 2 minutes. Calculate power. - Step 1: Convert units: $4800\,J$ and $120\,s$ . - Step 2: $P = E / t = 4800 / 120 = 40\,W$ .
Q1: Describe how energy is transferred through a solid by heating. What is the name of this effect? - Answer: Energy is transferred as particles vibrate and collide, passing kinetic energy to neighbors. This is called conduction.
Q1: Explain how cavity wall insulation reduces energy transfer out of a house. - Answer: The air gap in a cavity wall reduces energy loss by conduction. Filling the gap with foam (insulation) prevents convection currents from developing in the gap.
Q1: A motor transfers 300 J into car stores; 225 J is kinetic. Calculate efficiency. - Answer: $\text{Efficiency} = \frac{225}{300} = 0.75$ or $75\%$ .
Q2: A machine has 900 W useful output and 1200 W total input. 72 kJ is transferred to it. Calculate useful energy transferred. - Step 1: Efficiency = $900 / 1200 = 0.75$ . - Step 2: Useful energy = $0.75 \times 72,000\,J = 54,000\,J$ or $54\,kJ$ .