understand that (thermal) energy is transferred from a region of higher temperature to a region of lower temperature

Published by Patrick Mutisya · 14 days ago

Cambridge A-Level Physics 9702 – Thermal Equilibrium

Thermal Equilibrium

Learning Objective

Understand that (thermal) energy is transferred from a region of higher temperature to a region of lower temperature until thermal equilibrium is reached.

Key Concepts

  • Temperature: a measure of the average kinetic energy of the particles in a system.

  • Thermal Energy: the total internal kinetic energy of the particles in a body.

  • Heat Transfer: the process by which thermal energy moves from one region to another.

  • Thermal Equilibrium: the state in which two or more objects in contact have the same temperature and no net heat flow occurs.

Mechanisms of Heat Transfer

  1. Conduction – direct transfer through a material.

  2. Convection – transfer by bulk movement of fluid.

  3. Radiation – transfer by electromagnetic waves.

Quantitative Description

The amount of thermal energy transferred as heat, \$Q\$, can be expressed by:

\$Q = mc\Delta T\$

where

  • \$m\$ is the mass of the object,

  • \$c\$ is the specific heat capacity,

  • \$\Delta T = T{\text{final}} - T{\text{initial}}\$ is the change in temperature.

For conduction through a uniform rod of length \$L\$ and cross‑sectional area \$A\$, Fourier’s law gives the rate of heat flow:

\$\frac{dQ}{dt} = -kA\frac{dT}{dx}\$

where \$k\$ is the thermal conductivity of the material.

Illustrative Example

Two metal blocks, A and B, are placed in contact. Block A is initially at \$80^\circ\text{C}\$ and block B at \$20^\circ\text{C}\$. Assuming no heat loss to the surroundings, heat will flow from A to B until both reach a common temperature \$T_{\text{eq}}\$.

Using conservation of energy:

\$mAcA(T{\text{eq}}-80) + mBcB(T{\text{eq}}-20) = 0\$

Solving for \$T_{\text{eq}}\$ gives the equilibrium temperature.

Common Misconceptions

  • Heat is a substance that flows; actually, heat is energy transferred due to a temperature difference.

  • Temperature and thermal energy are the same; temperature is an intensive property, while thermal energy is extensive.

  • Heat always flows from hot to cold regardless of the medium; the rate depends on the medium’s properties (conductivity, convection currents, emissivity).

Summary Table

PhenomenonDirection of Energy TransferTypical EquationKey Parameter
ConductionFrom higher to lower temperature region within a solid\$\frac{dQ}{dt} = -kA\frac{dT}{dx}\$Thermal conductivity \$k\$
ConvectionVia moving fluid parcels\$Q = hA(T{\text{surface}}-T{\text{fluid}})\$Heat transfer coefficient \$h\$
RadiationThrough empty space\$Q = \varepsilon\sigma A(T^4{\text{hot}}-T^4{\text{cold}})\$Emissivity \$\varepsilon\$ and Stefan‑Boltzmann constant \$\sigma\$

Suggested diagram: Two blocks of different temperatures placed in contact, showing arrows indicating heat flow from the hotter block to the cooler block until equilibrium is reached.

Questions for Revision

  1. Explain why heat flows spontaneously from a hotter object to a colder one, referencing the second law of thermodynamics.

  2. Derive the equilibrium temperature for two objects of different masses, specific heats, and initial temperatures when they are placed in thermal contact.

  3. Identify which mode of heat transfer dominates in the following situations and justify your answer:

    • A metal spoon in a cup of hot tea.

    • Warm air rising in a room.

    • The Sun heating the Earth.