Ch 4 · 2.2.2 Specific Heat Capacity · O Level Physics 5054
Topic 4 of 9 in Thermal Physics — O Level Physics 5054 — 40 lessons.
Introduction
On a sunny day the sand on a beach burns your feet, but the sea stays cool. The Sun gives them the same energy per square metre, yet the sand warms up far more. The difference is specific heat capacity: how much energy each kilogram of a material needs for each degree of temperature rise. (Syllabus section 2.2.2.)
Key ideas — Temperature and internal energy
The particles in an object have kinetic energy (they move or vibrate) and potential energy (from the forces between them). Together this is the object's internal energy (its thermal energy store).
🧑🏫 Teacher's explanation
Imagine a crowded dance floor. The 'internal energy' is the total amount of energy possessed by every single person on that floor. Some people are dancing wildly (high kinetic energy), while others are just standing close together (potential energy). If the music speeds up and everyone starts moving faster, the total energy of the room increases. In physics, temperature is simply a measure of how fast the particles in a substance are moving or vibrating on average.
📖 Definitions
🔍 Worked example — Easy
Calculate the energy required to raise the temperature of 0.5 kg of water from 20circC to 50circC. The specific heat capacity of water is 4200 J/(kgcircC).
🔍 Worked example — Standard
A 2.0 kg block of metal absorbs 12,000 J of thermal energy, and its temperature increases by 15circC. Calculate the specific heat capacity of the metal.
🔍 Worked example — Exam-style
An electric heater provides 5000 J of energy to a 0.2 kg copper block. The temperature rises from 25circC to 45circC. Calculate the specific heat capacity of copper.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — What temperature means for particles
A rise in temperature means the average kinetic energy of all the particles in the object has increased: on average they move or vibrate faster.
🧑🏫 Teacher's explanation
Imagine a crowded dance floor. If everyone is standing still or swaying gently, the 'energy' of the room is low. If suddenly everyone starts dancing wildly and bumping into each other with more speed, the room feels much more energetic. In physics, temperature is simply a measure of how much 'dancing' (kinetic energy) the particles in a substance are doing on average.
📖 Definitions
🔍 Worked example — Easy
A 0.5 kg block of metal absorbs 2500 J of thermal energy, and its temperature rises by 10 °C. Calculate the specific heat capacity of the metal.
🔍 Worked example — Standard
How much energy is required to raise the temperature of 2.0 kg of water from 20 °C to 50 °C? (Specific heat capacity of water is 4200 J/(kg °C)).
🔍 Worked example — Exam-style
An electric heater supplies 15,000 J of energy to a 0.2 kg copper block. The temperature increases from 25 °C to 75 °C. Calculate the specific heat capacity of copper.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Specific heat capacity
The specific heat capacity c of a substance is the energy required per unit mass per unit temperature increase: the energy needed to raise the temperature of 1 kg of it by 1 °C.
🧑🏫 Teacher's explanation
Imagine you have two identical-looking blocks: one made of iron and one made of wood. If you leave them both in the sun for ten minutes, the iron block will feel much hotter to the touch. This is because different materials require different amounts of energy to change their temperature. Some materials are 'stubborn' and resist temperature changes, while others change temperature very easily.
📖 Definitions
🔍 Worked example — Easy
Calculate the energy required to raise the temperature of 2.0 kg of water from 20 °C to 30 °C. (Specific heat capacity of water = 4200 J/(kg °C))
🔍 Worked example — Standard
An electric heater supplies 15,000 J of energy to a 0.5 kg block of aluminium. Calculate the rise in temperature of the block. (Specific heat capacity of aluminium = 900 J/(kg °C))
🔍 Worked example — Exam-style
A 500 g piece of copper is heated from 25 °C to 75 °C. Calculate the specific heat capacity of the copper if 12,500 J of energy was transferred. (Note: convert mass to kg first)
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Practical notes
Measuring the specific heat capacity of a solid (a metal block with two holes).
Worked example
Example 1. A heater supplies 168 000 J to 0.50 kg of water. The temperature rises from 20 °C to 100 °C. Find the specific heat capacity of water from these results.
🔍 Worked example — Easy
A 2.0 kg block of metal absorbs 4400 J of thermal energy, and its temperature increases by 5.0 °C. Calculate the specific heat capacity of the metal.
🔍 Worked example — Standard
A 0.50 kg container of oil is heated from 25 °C to 75 °C. If 12,000 J of energy is supplied, calculate the specific heat capacity of the oil.
🔍 Worked example — Exam-style
An electric heater with a power rating of 120 W is used to heat 0.20 kg of a liquid. The temperature of the liquid rises by 40 °C in 300 s. Calculate the specific heat capacity of the liquid, assuming no heat is lost to the surroundings.
⚠️ Common errors
Common mistakes
Practice
Answers: (1) The energy required per unit mass per unit temperature increase. (2) Δ E = 2.0 × 900 × 50 = 90 000\ J. (3) Δθ = 33 600/0.20 × 4200 = 40\ ^circC. (4) To reduce energy lost to the surroundings, so that nearly all the energy supplied raises the block's temperature.