Energy changes in systems: temperature change, ∆θ, in degrees Celsius, °C

The idea

Temperature change, ∆θ, is the difference between the final and initial temperatures of a system, measured in degrees Celsius, °C. You calculate it as ∆θ = θ_final − θ_initial. For example, if water warms from 20 °C to 65 °C, ∆θ = 65 − 20 = 45 °C. In E = mc∆θ, ∆θ must be the change in temperature, not the final temperature alone. A fall in temperature gives a negative ∆θ, meaning energy is transferred away from the system. The degree Celsius is the same size as the kelvin, so a temperature change of 45 °C equals a change of 45 K, but temperatures themselves are not interchangeable without conversion.

What earns the marks

• Calculate temperature change as final temperature minus initial temperature, ∆θ = θ_final − θ_initial.
• Use degrees Celsius, °C, as the unit for temperature change in energy calculations.
• Substitute ∆θ correctly into E = mc∆θ, keeping the sign to show a rise or fall in temperature.
• Recognise that a temperature fall gives a negative ∆θ and therefore a negative energy change, indicating energy transfer out of the system.
• State that a temperature change of 1 °C is the same size as a temperature change of 1 K.
• Read thermometers or data tables accurately to obtain initial and final temperatures before subtracting.

Common mistakes and how to put them right

• Using the final temperature instead of the change in temperature.

  Put it right: Subtract the initial temperature from the final temperature.

• Adding the initial and final temperatures instead of subtracting.

  Put it right: ∆θ is a difference, so use θ_final − θ_initial.

• Mixing up temperature and temperature change when using kelvin.

  Put it right: A change of 45 °C equals 45 K, but 45 °C is not 45 K as an absolute temperature.

Exam tips

• Underline the initial and final temperatures in the question before subtracting so you do not use the wrong values.
• Show the subtraction in your working, for example ∆θ = 65 − 20 = 45 °C, to make your method clear.
• If a temperature falls, keep the negative sign in ∆θ and interpret the negative energy value as energy transferred away from the substance.