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2.4 Specific Heat Capacity

GCSE Physics · AQA · Chapter 2: Energy Transfer by Heating

A free GCSE Physics lesson for AQA (8463) from OBA School: what specific heat capacity means, using ΔE = m c Δθ, the effect of mass, and storage heaters. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • State the factors that affect the temperature rise of a substance when it is heated
  • Define specific heat capacity and give its unit
  • Use ΔE = m c Δθ, rearranging it to find any quantity
  • Explain how the mass of an object affects how quickly its temperature changes
  • Explain uses of materials with a high specific heat capacity, such as water and storage heater bricks

Key words

  • Specific heat capacity, c: The energy needed to raise the temperature of 1 kg of a substance by 1 °C. Unit: J/kg °C.
  • Thermal energy store: The store that increases when an object’s temperature rises.
  • Temperature change, Δθ: Final temperature minus starting temperature, in °C. (Δ means “change in”; θ is “theta”.)
  • Energy transferred, ΔE: The change in the thermal energy store, in joules (J).
  • Storage heater: A heater with a core of bricks or concrete that is heated at night and releases energy during the day.

What decides the temperature rise?

When you heat something, the energy transferred to it increases its thermal energy store and its temperature rises. How much it rises depends on:

  • the energy transferred to it
  • its mass
  • the substance it is made of.

For the same energy input, a larger mass warms up more slowly (and cools down more slowly), because the energy is shared among more particles. Different substances also need different amounts of energy per kilogram for each degree – this is their specific heat capacity.

Specific heat capacity and the equation

The specific heat capacity of a substance is the energy needed to raise the temperature of 1 kg of the substance by 1 °C. Water has a very high value: 4200 J is needed for each kilogram and each degree.

change in thermal energy = mass × specific heat capacity × temperature change

ΔE = m c Δθ

ΔE in joules (J) · m in kilograms (kg) · c in joules per kilogram per degree Celsius (J/kg °C) · Δθ in degrees Celsius (°C)

Rearranged: c = ΔE ÷ (m Δθ) Δθ = ΔE ÷ (m c) m = ΔE ÷ (c Δθ)

Exam tip: The equation will be on your equation sheet, but you must choose it, convert units (g → kg, kJ → J) and rearrange it yourself.

Using ΔE = m c Δθ

Worked example: energy needed

How much energy heats 2.5 kg of water from 18 °C to 65 °C? (c = 4200 J/kg °C)
Δθ = 65 − 18 = 47 °C
ΔE = m c Δθ = 2.5 × 4200 × 47 = 493 500 J

Answer: 494 000 J = 494 kJ (to 3 s.f.)

Worked example: temperature rise

A 1.5 kg aluminium block (c = 900 J/kg °C) gains 45 kJ. Find its temperature rise.
ΔE = 45 kJ = 45 000 J
Δθ = ΔE ÷ (m c) = 45 000 ÷ (1.5 × 900) = 33.3 °C

Answer: 33 °C

Worked example: finding c

A 800 g metal block warms from 20 °C to 40 °C when 7.2 kJ is transferred to it.
m = 800 g = 0.800 kg; Δθ = 20 °C; ΔE = 7200 J
c = ΔE ÷ (m Δθ) = 7200 ÷ (0.800 × 20) = 450 J/kg °C

Answer: 450 J/kg °C (close to the value for iron)

Worked example: heating water in a pan

0.60 kg of water in a 0.25 kg aluminium pan is heated from 20 °C to 100 °C.
water: 0.60 × 4200 × 80 = 201 600 J
pan: 0.25 × 900 × 80 = 18 000 J
total = 201 600 + 18 000 = 219 600 J

Answer: about 220 kJ – both the water and the pan must be heated

Linking with power

An electric heater transfers energy E = P t (P in watts, t in seconds). If no energy is wasted, P t = m c Δθ.

Worked example: how long a kettle takes

A 2400 W kettle heats 1.0 kg of water from 20 °C to 100 °C. Assume no energy is wasted.
ΔE = 1.0 × 4200 × 80 = 336 000 J
t = E ÷ P = 336 000 ÷ 2400 = 140 s

Answer: 140 s (in reality a bit longer, because some energy heats the kettle and the air)

Using a high specific heat capacity

  • Water stores a lot of energy for each degree, so it is used in central heating systems and car cooling systems, and hot water bottles stay warm for a long time.
  • Storage heaters contain bricks or concrete with a high specific heat capacity. Cheaper off-peak electricity heats them at night; they store a lot of energy, warm up slowly and cool down slowly, releasing energy to the room through the day.

You can measure the specific heat capacity of a metal block yourself – see the required practical in section 2.7.

Common mistakes

  • Using the final temperature instead of the temperature change for Δθ.
  • Leaving mass in grams or energy in kilojoules. Convert to kg and J first.
  • Rearranging wrongly: c = ΔE ÷ (m × Δθ) – divide by both m and Δθ.
  • Thinking a high specific heat capacity means a substance gets hot quickly. It is the opposite: it warms up slowly.

Revision questions

Try these, then check your answers below each one.

Question 1. What is the specific heat capacity of a substance? (Choose from: the energy needed to raise the temperature of 1 kg of it by 1 °C, the energy needed to melt 1 kg of it, the temperature rise of 1 kg of it when 1 J is supplied, the energy stored in 1 kg of it at room temperature.)

Answer: the energy needed to raise the temperature of 1 kg of it by 1 °C

Working: Specific heat capacity = energy per kilogram per degree Celsius of temperature rise.

Question 2. Calculate the energy needed to heat 2.0 kg of water from 15 °C to 35 °C. (c = 4200 J/kg °C)

Answer: 168000 J

Working: Δθ = 35 − 15 = 20 °C. ΔE = 2.0 × 4200 × 20 = 168 000 J.

Question 3. A 3.0 kg aluminium block is given 54 kJ of energy. Calculate its temperature rise. (c = 900 J/kg °C)

Answer: 20 °C

Working: Δθ = ΔE ÷ (m c) = 54 000 ÷ (3.0 × 900) = 20 °C.

Related lessons

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This lesson is section 2.4 (AGCPH0204) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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