Specific heat capacity Revision Notes

Internal energy is the total energy stored within a system due to the kinetic energy of its particles (their motion) and the potential energy from the forces between particles.

Temperature is a measure of the average kinetic energy of the particles in a substance. It indicates how hot or cold the object is but does not measure total energy directly.

The SI unit of temperature is the degree Celsius (°C) or kelvin (K), where 0 K is absolute zero, the theoretical point where particles have minimum kinetic energy.

• Internal energy includes both kinetic and potential energy of particles.
• Temperature reflects average kinetic energy of particles.
• Units: temperature in °C or K; internal energy in joules (J).

When an object is heated, energy is transferred to its particles, causing them to move faster on average.

This increase in particle speed means their average kinetic energy rises.

Since temperature is proportional to average kinetic energy, the temperature of the object increases as the particles move more rapidly.

• Heating transfers energy to particles.
• Particle speed and kinetic energy increase.
• Temperature rises as a result.

The internal energy of an object increases when its temperature rises because the particles have more kinetic energy.

This means the total energy stored inside the object is higher after heating.

The increase in internal energy is directly related to the temperature change, assuming no phase change occurs (e.g., melting or boiling).

• Internal energy increases with temperature.
• Energy is stored in particle motion and interactions.
• No phase change means temperature and internal energy rise together.

Internal energy consists of two main components: the kinetic energy of particles (due to their motion) and the potential energy (due to forces between particles).

When temperature increases, the kinetic energy component increases.

Potential energy changes mainly during phase changes, not during simple temperature rises.

• Kinetic energy increases with temperature.
• Potential energy remains mostly constant unless phase changes occur.
• Internal energy = kinetic energy + potential energy.

Understanding the link between temperature and internal energy is essential in thermal physics, including heat transfer and specific heat capacity.

It explains why heating an object increases its stored energy and why temperature is a useful indicator of this energy change.

This concept underpins calculations involving energy transfer in heating and cooling processes.

• Temperature rise indicates increased internal energy.
• Essential for understanding heat transfer.
• Basis for specific heat capacity calculations.

Temperature is a physical quantity that measures the average kinetic energy of the particles in a substance. Particles include atoms or molecules that make up solids, liquids, and gases.

The kinetic energy of a particle is the energy it possesses due to its motion. In thermal physics, this motion is random and includes translational, rotational, and vibrational movements depending on the state of matter.

The average kinetic energy per particle is directly proportional to the temperature measured in kelvin (K). This means that as temperature increases, the particles move faster on average, increasing their kinetic energy.

• Temperature (T) is measured in kelvin (K).
• Average kinetic energy (KE_avg) of particles is proportional to T.
• Particles move faster as temperature rises.

The kinetic energy (KE) of a single particle moving with speed v and mass m is given by the formula:

\[ KE = \frac{1}{2} m v^2 \] where m is the mass of the particle and v is its speed.

When the temperature of an object rises, the average speed of its particles increases, so the average kinetic energy increases accordingly. This increase in kinetic energy is the microscopic cause of the temperature rise observed macroscopically.

• KE = ½ mv² for each particle.
• Average particle speed increases with temperature.
• Temperature rise means increase in average KE of particles.

In solids, particles vibrate about fixed positions. As temperature rises, the amplitude and speed of these vibrations increase, raising the average kinetic energy.

In liquids and gases, particles move more freely. A temperature increase means particles move faster and collide more energetically.

This microscopic increase in particle motion manifests as a measurable temperature rise, which can be detected by thermometers and other temperature sensors.

• Solids: increased vibration speed and amplitude.
• Liquids and gases: increased particle speed and collision energy.
• Temperature rise reflects increased particle motion.

The internal energy of an object includes the total kinetic energy of its particles. When heat energy is supplied, it increases the internal energy, raising the temperature and thus the average kinetic energy of particles.

This relationship explains why heating an object causes its temperature to rise: energy transferred as heat increases particle motion.

Understanding this link is fundamental to concepts such as specific heat capacity and thermal expansion.

• Internal energy includes kinetic energy of particles.
• Heat transfer increases particle kinetic energy.
• Temperature rise indicates increased internal energy.

A useful diagram to illustrate this concept is a set of particle models at two different temperatures:

At lower temperature, particles are shown moving slowly with shorter arrows indicating velocity.

At higher temperature, particles have longer arrows showing increased speed and kinetic energy.

• Draw two boxes labelled 'Low Temperature' and 'High Temperature'.
• Inside each, draw several circles representing particles.
• Add velocity arrows: short arrows for low T, longer arrows for high T.
• This visually links temperature to particle kinetic energy.

Specific heat capacity, denoted by the symbol c, is a physical property of a substance that quantifies the amount of thermal energy required to raise the temperature of a unit mass of the substance by one degree Celsius (or one kelvin).

It is defined as the energy needed to raise the temperature of 1 kilogram of a material by 1 °C (or 1 K).

Mathematically, specific heat capacity is given by the formula: c = ΔE / (m Δθ), where: ΔE is the thermal energy supplied (in joules, J), m is the mass of the substance (in kilograms, kg), and Δθ is the temperature change (in degrees Celsius, °C, or kelvin, K).

• Specific heat capacity (c) units: joules per kilogram per degree Celsius (J/kg °C) or joules per kilogram per kelvin (J/kg K).
• Temperature change Δθ can be in °C or K since the size of one degree is the same in both scales.

Rearranging the definition formula gives the equation for the thermal energy transferred to or from a substance when its temperature changes: ΔE = mcΔθ.

This equation states that the energy supplied (or removed) is equal to the product of the mass, specific heat capacity, and temperature change.

This relationship assumes no change of state (no melting or boiling) and that all energy goes into changing the temperature (internal energy) of the substance, not into work or phase change.

• ΔE: energy transferred (J)
• m: mass of the substance (kg)
• c: specific heat capacity (J/kg °C)
• Δθ: temperature change (°C or K)

Calculate the energy required to raise the temperature of 2.0 kg of water from 20 °C to 80 °C. The specific heat capacity of water is 4200 J/kg °C.

Step 1: Identify known values: m = 2.0 kg, c = 4200 J/kg °C, initial temperature θ₁ = 20 °C, final temperature θ₂ = 80 °C.

Step 2: Calculate temperature change: Δθ = θ₂ - θ₁ = 80 - 20 = 60 °C (or K). Step 3: Use the formula ΔE = mcΔθ: ΔE = 2.0 × 4200 × 60 = 504,000 J (or 5.04 × 10⁵ J). Step 4: State the answer with units: The energy required is 5.04 × 10⁵ joules.

• Common error: forgetting to convert mass to kilograms if given in grams.
• Ensure temperature change is calculated correctly (final minus initial).
• Use consistent units throughout the calculation.

To illustrate the concept, draw a labelled diagram showing: A block representing the substance (e.g., water).

An arrow labelled ΔE pointing towards the block to indicate energy supplied (in joules). Below the block, label the mass m (kg). To the right, indicate the temperature change Δθ (°C). Above or inside the block, write the specific heat capacity c (J/kg °C). This visual helps link the variables in the formula ΔE = mcΔθ.

• Use clear, straight arrows to represent energy transfer.
• Label all quantities with correct symbols and units.
• Include a temperature scale or thermometer symbol to indicate temperature change.

In experiments to determine specific heat capacity, measure the mass of the substance, the temperature change using a thermometer, and the energy supplied using an electrical heater and a joulemeter or by measuring current, voltage, and time.

Repeat measurements to improve accuracy and calculate an average.

In exams, always: write the formula used, substitute values with units, show rearrangement if needed, and give the final answer with correct units and significant figures.

• Check units carefully to avoid errors.
• Remember that specific heat capacity is a scalar quantity.
• Do not confuse specific heat capacity with heat capacity (which is for the whole object).

Specific heat capacity, denoted by \( c \), is defined as the amount of heat energy required to raise the temperature of 1 kilogram of a substance by 1 degree Celsius (or 1 kelvin).

The relationship between heat energy supplied \( Q \), mass \( m \), specific heat capacity \( c \), and temperature change \( \Delta T \) is given by the formula:

\[ Q = mc\Delta T \] where: \( Q \) is in joules (J), \( m \) is in kilograms (kg), \( c \) is in joules per kilogram per degree Celsius (J/kg°C), and \( \Delta T \) is in degrees Celsius (°C).

• Specific heat capacity \( c \) has units J/kg°C.
• Heat energy \( Q \) can be supplied electrically or by combustion.
• Temperature change \( \Delta T = T_{final} - T_{initial} \).

This method uses electrical heating to supply a known amount of energy to a solid and measures the resulting temperature change.

Apparatus needed: a solid sample (e.g., a metal block), an electric heater (immersion heater or heating coil), a power supply, an ammeter, a voltmeter, a thermometer or thermocouple, a stopwatch, and a balance to measure mass.

Procedure: 1. Measure the mass \( m \) of the solid using the balance. 2. Connect the heater to the power supply and insert it into the solid. 3. Record the initial temperature \( T_{initial} \) of the solid. 4. Switch on the heater and simultaneously start the stopwatch. 5. Measure the current \( I \) through the heater and the potential difference \( V \) across it using the ammeter and voltmeter. 6. After a set time \( t \) (e.g., 5 minutes), switch off the heater and record the final temperature \( T_{final} \). 7. Calculate the electrical energy supplied using \( Q = IVt \). 8. Calculate the temperature change \( \Delta T = T_{final} - T_{initial} \). 9. Calculate the specific heat capacity using \( c = \frac{Q}{m\Delta T} \).

• Independent variable: time heater is on (or energy supplied).
• Dependent variable: temperature change of the solid.
• Control variables: mass of solid, initial temperature, heater power.
• Repeat measurements to improve reliability.
• Ensure good thermal contact between heater and solid.
• Minimise heat loss by insulating the solid (e.g., with a wool jacket).

This method uses a calorimeter to measure the temperature change when a known amount of heat is supplied to a liquid.

Apparatus needed: a calorimeter (e.g., a copper can), a thermometer, a balance, a heater or a known mass of hot water, a stirrer, and a stopwatch.

Procedure: 1. Measure the mass \( m \) of the liquid by weighing the calorimeter empty and then with the liquid; subtract to find liquid mass. 2. Record the initial temperature \( T_{initial} \) of the liquid. 3. Supply a known amount of heat to the liquid, either by electrical heating (using the method above) or by mixing with a known mass of hot water at a known temperature. 4. Stir the liquid gently to ensure uniform temperature. 5. Record the highest temperature reached \( T_{final} \). 6. Calculate the temperature change \( \Delta T = T_{final} - T_{initial} \). 7. Calculate the heat energy supplied \( Q \) (from electrical energy or heat transfer from hot water). 8. Calculate the specific heat capacity using \( c = \frac{Q}{m\Delta T} \).

• Independent variable: heat energy supplied.
• Dependent variable: temperature change of the liquid.
• Control variables: mass of liquid, initial temperature, insulation of calorimeter.
• Repeat to improve accuracy.
• Use a lid to reduce heat loss.
• Stir to ensure even temperature distribution.

Example: A 0.5 kg metal block is heated by an electric heater supplying 12 V and 2 A for 300 seconds. The temperature rises from 20°C to 50°C. Calculate the specific heat capacity.

Step 1: Calculate electrical energy supplied: \( Q = IVt = 12 \times 2 \times 300 = 7200 \, \text{J} \).

Step 2: Calculate temperature change: \( \Delta T = 50 - 20 = 30 \, ^\circ\text{C} \). Step 3: Calculate specific heat capacity: \[ c = \frac{Q}{m\Delta T} = \frac{7200}{0.5 \times 30} = \frac{7200}{15} = 480 \, \text{J/kg}^\circ\text{C} \] This is the specific heat capacity of the metal block.

• Show all units in calculations.
• Rearrange formula as needed: \( c = \frac{Q}{m\Delta T} \).
• Common error: forgetting to convert mass to kilograms or time to seconds.
• Check that temperature change is positive and sensible.

Heat loss to the surroundings causes errors; minimise this by insulating the solid or using a calorimeter with a lid.

Repeat measurements and calculate an average to reduce random errors.

Use a digital thermometer or thermocouple for more precise temperature readings than a mercury thermometer if available, especially for small temperature changes or liquids with low specific heat capacity. Safety precautions include handling hot equipment carefully, using heat-resistant gloves, and ensuring electrical equipment is properly insulated and switched off when not in use.

• Insulate apparatus to reduce heat loss.
• Repeat and average results for reliability.
• Use appropriate protective equipment.
• Handle electrical equipment safely.
• Avoid overheating to prevent damage or burns.