Specific Heat Capacity Calculator

GCSE PhysicsAQAEdexcelOCRFoundation & Higher

Find the energy, mass, specific heat capacity or temperature change using ΔE = m c Δθ. Enter the temperature change, not the final temperature.

Quick answer

Change in thermal energy = mass × specific heat capacity × temperature change. Use mass in kg and c in J/kg °C to get joules. For example, heating 2.0 kg of water by 15 °C takes ΔE = 2.0 × 4200 × 15 = 126,000 J.

By Mehmood Kakar · Updated

ΔE = m × c × Δθ
Find:

Water is 4200 J/kg °C. Use the value given in the question.

Temperature change = final temperature − starting temperature.

How to use the specific heat capacity equation

Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 °C. Water's is 4200 J/kg °C, which is why it takes so long to boil a full kettle. On your equation sheet the equation is:

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

  • ΔE is the change in thermal energy in joules (J)
  • m is mass in kilograms (kg)
  • c is specific heat capacity in joules per kilogram per degree Celsius (J/kg °C)
  • Δθ is the temperature change in degrees Celsius (°C)

Δθ is the change in temperature. If water is heated from 20 °C to 100 °C, Δθ is 80 °C, not 100 °C. A change of 1 °C is the same size as a change of 1 K, so either unit works for Δθ.

A material with a low specific heat capacity, such as aluminium (about 900 J/kg °C), warms up quickly. Water's high value makes it good for storing thermal energy in radiators and hot water bottles.

This equation is behind the specific heat capacity required practical. You heat a block with an electric heater, measure the energy supplied and the temperature rise, then rearrange to find c = ΔE ÷ (m × Δθ). Your measured value usually comes out higher than the true value, because some energy heats the surroundings instead of the block.

Common mistakes that cost marks

  1. Using the final temperature instead of the change. Heating from 20 °C to 100 °C is a change of 80 °C.
  2. Leaving mass in grams. 500 g is 0.5 kg. Divide by 1000.
  3. Mixing kJ and J. If energy is given in kJ, convert to J before finding c, or your answer will be 1000 times too small.
  4. Dividing by only one quantity. To find c, divide ΔE by m and by Δθ: c = ΔE ÷ (m × Δθ).
  5. Writing the unit wrongly. The unit of c is J/kg °C. Don’t leave out the °C.

Practice questions

Try each one on paper first, then reveal the worked answer.

Q12.0 kg of water is heated so its temperature rises by 15 °C. The specific heat capacity of water is 4200 J/kg °C. Calculate the energy transferred.[2 marks]
  1. ΔE = m × c × Δθ
  2. ΔE = 2.0 × 4200 × 15
  3. ΔE = 126,000 J (126 kJ)
Q2A 0.50 kg metal block is heated with 9000 J of energy. Its temperature rises by 20 °C. Calculate the specific heat capacity of the metal.[3 marks]
  1. Rearrange: c = ΔE ÷ (m × Δθ)
  2. c = 9000 ÷ (0.50 × 20)
  3. c = 9000 ÷ 10
  4. c = 900 J/kg °C
Q3A kettle heats 1.5 kg of water from 20 °C to 100 °C. The specific heat capacity of water is 4200 J/kg °C. Calculate the energy needed.[3 marks]
  1. Temperature change: Δθ = 100 − 20 = 80 °C
  2. ΔE = m × c × Δθ
  3. ΔE = 1.5 × 4200 × 80
  4. ΔE = 504,000 J (504 kJ)

Frequently asked questions

What is specific heat capacity?

It is the amount of energy needed to raise the temperature of 1 kg of a substance by 1 °C. For water it is 4200 J/kg °C.

What is the unit of specific heat capacity?

Joules per kilogram per degree Celsius, written J/kg °C. You may also see J/kg K, which has the same value because a change of 1 K equals a change of 1 °C.

Is Δθ the final temperature?

No. Δθ is the temperature change: final temperature minus starting temperature.

Why is the measured specific heat capacity often too high in the required practical?

Some of the energy from the heater warms the air and the apparatus instead of the block, so the temperature rise is smaller than it should be. Insulating the block reduces this.