Energy changes by heating and work

Where:

• $\Delta E$ = change in thermal energy in Joules ($J$)
• $m$ = mass in kilograms ($kg$)
• $c$ = specific heat capacity in Joules per kilogram per degree Celsius ($J/kg\text{ }°C$)
• $\Delta \theta$ = temperature change in degrees Celsius ($°C$)

Calculate the energy required to heat a $1.5\text{ kg}$ concrete block by $12\text{ °C}$. (Specific heat capacity of concrete = $880\text{ J/kg °C}$)

Step 1: Identify the known variables.

• $m = 1.5\text{ kg}$
• $c = 880\text{ J/kg °C}$
• $\Delta \theta = 12\text{ °C}$

Step 2: Substitute the values into the formula.

• $\Delta E = 1.5 \times 880 \times 12$

Step 3: Calculate the final answer with units.

• $\Delta E = 15,840\text{ J}$

Energy Transfer by Heating Pathways

Why does a metal spoon feel cold when you first pick it up, but quickly warms in your hand? Energy naturally transfers from a hotter object (the source) to a cooler object (the sink). This transfer continues until both objects reach the exact same temperature, a state known as thermal equilibrium.

The OCR specification identifies two primary heating pathways. Heating by particles includes conduction (energy transfer via direct contact and particle vibration) and convection (where hot regions in fluids rise and cold regions sink). Heating by radiation involves energy transfer via infrared electromagnetic waves; unlike conduction or convection, radiation does not require any physical medium or particles to travel through.

Any energy transferred to non-useful stores—typically the thermal store of the surroundings—is described as dissipated or wasted energy. Materials with low thermal conductivity transfer energy slowly and are used as insulation to reduce this dissipation.

Energy Transfer by Mechanical Work

Pushing a broken-down car along a flat road requires a huge amount of effort, transferring energy from your muscles into the car's motion. Work done occurs whenever a force makes an object move over a distance. This process transfers energy from one store to another via the mechanical pathway.

The amount of energy transferred is exactly equal to the work done. One Joule ($1\text{ J}$) of energy is transferred when a force of one Newton ($1\text{ N}$) moves an object by one metre ($1\text{ m}$). If a force is applied but the object remains perfectly stationary, the work done is $0\text{ J}$.

Where:

• $W$ = Work done in Joules ($J$)
• $F$ = Force in Newtons ($N$)
• $s$ = Distance (or displacement) in metres ($m$)

A crane lifts a steel beam with a weight of $4,500\text{ N}$ vertically upwards by $12\text{ m}$. Calculate the work done.

Step 1: Identify the known variables.

• $F = 4,500\text{ N}$
• $s = 12\text{ m}$

Step 2: Substitute the values into the formula.

• $W = 4,500 \times 12$

Step 3: Calculate the final answer with units.

• $W = 54,000\text{ J}$ (or $54\text{ kJ}$)

When describing energy changes, you must identify the full sequence. For example, when a car brakes, energy is transferred from the kinetic store of the car, via the mechanical pathway, to the thermal store of the brakes and surroundings (due to friction).

Energy Transfer by Electrical Work

Every time you switch on your smartphone, a tiny battery forces electrons through microscopic circuits to power the screen. Electrical work is done when a charge moves through a potential difference in a closed circuit. This transfers energy from a power supply to components via the electrical pathway.

As an electric current flows, moving electrons continuously collide with vibrating positive ions in the metal lattice of the wire. These collisions transfer kinetic energy from the electrons to the ions, increasing the thermal store of the wire (a heating effect). The total energy supplied by the power source is always equal to the useful energy transferred plus the energy dissipated to the surroundings.

Where:

• $E$ = Energy transferred in Joules ($J$)
• $V$ = Potential difference in Volts ($V$)
• $I$ = Current in Amperes ($A$)
• $t$ = Time in seconds ($s$)

A $12\text{ V}$ motor draws a current of $3\text{ A}$ for $45\text{ s}$. Calculate the total energy transferred.

Step 1: Identify the known variables.

• $V = 12\text{ V}$
• $I = 3\text{ A}$
• $t = 45\text{ s}$

Step 2: Substitute the values into the formula.

• $E = 12 \times 3 \times 45$

Step 3: Calculate the final answer with units.

• $E = 1,620\text{ J}$

When describing energy transfers in an electrical circuit, follow the step-by-step path. In a battery-powered lamp, energy moves from the chemical store of the battery $\rightarrow$ along the electrical pathway $\rightarrow$ to the thermal store of the filament $\rightarrow$ before being transferred to the surroundings via radiation (light) and heating by particles.