⇒ When substances are heated, thermal energy is supplied to the particles of the substance, incresing their internal energy (U), and therefore the average kinetic energy of the particles

⇒ Increasing the average kinetic energy of the particles causes the temperature of the particles to rise

⇒ The size of the temperature change, Δθ, is dictated by several macroscopic measurable factors: the amount of thermal heat energy supplied, Q; the mass of the substance, m; and a quantity called the specific heat capacity of the substance, c, which is unique to each substance; and its state

⇒ These factors are related to each other by the equation: Q = mcΔθ

⇒ The thermal energy Q is measured in joules (J), the mass m is measured in kilograms (kg), and the temperature change Δθ is measured in kelvin (K), so the units of specific heat capacity, c, are Jkg^-1K^-1

⇒ The specific heat capacity of a material is a fundamental property of the material and is particulalry important to engineers and scientists designing engines and insulation systems

⇒ A specific heat capactiy dictates how easy it is for a material to change its temperature

⇒ Materials with very high specific heat capacities, such as water, C_w = 4186Jkg^-1K^-1, require only a small quantity of thermal energy to increas the temperature of 1kg of the material by 1K, whereasmaterials such as gold with quite low specific heat cpacities, C_Au = 126Jkg^-1K^-1, require only a small quantity of thermal energy to increase the temperature of 1kg of the material by 1K

⇒ The specific heat capacity of a material enables us to measure the change in temperature of a material following a change in thermal energy

⇒ If a hot liquid or a solid is placed into a cold liquid, the internal energy transferred from the hot object when it cools down is equal to the thermal energy gained by the cold liquid and its container, plus the thermal energy lost to its surroundings

⇒ In this example, the thermal energy lost to the surrounding is assumed to be negligible:

⇒ The specific heat capacity of a fluid can be measured using a continuous flow method, where the fluid moves over an electric heater at a constant rate

⇒ It is assumed that the thermal energy transferred from the apparatus to the surroundings is constant

⇒ The experiment is carried out and then the flow rate of the fluid is changed, and then a second set of readinga is taken

⇒ The heat loss can then be eliminated from the calculations

⇒ A fluid flows through an insulated tube containing an electric heating wire

⇒ The rise in temperature of the fluid is measured by the two electronic thermometers and calculated by Δθ = T₂ - T₁

⇒ The mass of the fluid that flows through the apparatus in a time (t₁) is m₁, and is measured using a beaker on a balance and a stopwatch

⇒ The flow rate of the fluid is then altered to give another value, m₂, and the heater controls are changed to give the same temperature difference (Δθ)

⇒ The specific heat capacity of the fluid can then be determined by assuming that the thermal losses to the surroundings ar constant for both flow rates

⇒ For the first flow rate, the electrical energy supplied to the fluid in time t₁ is given by: I₁V₁t₁ = m₂cΔ&thea; + E_lost

• Where I₁ and V₁ are the inital current and potential difference of the heater and E_lost is the thermal energy lost to the surroundings

⇒ For the second flow rate: I₂V₂t₂ = m₂cΔ&thea; + E_lost

⇒ E_lost can be asumed to be the same in each experiment,so subtracting equation (ii) from equation (i) gives:

⇒ If the experiments are both run for the same time, t, then:

⇒ When liquids are heated up to their boiling point, the thermal energy is used to increase the internal energy of the molecules of the liquid

⇒ We measure this as temperature change

⇒ However, at the boiling point, the temperature change stops and all the thermal energy input is used to overcome the intermolecular forces between the particles of the liquid, converting it into a gas

⇒ The amount of thermal energy required to change the state of a substance, without a change in temperature, Q (in J), is given by: Q = ml

• Where m is the mass of the substance (in kg) and l is the specific latent heat (latent means 'hidden') of the substance (in J kg^-1)
• This equation applies to all the phase changes involved with changes of state
• So water, for example, has a specific latent heat of vaporisation, l_w, which deals with the phase change from liquid to gas (and vice versa), and a specific latent heat of fusion, l_f, which deals with the phase change from solid to liquid (and vice versa)

⇒ The relationship between the kinetic theoriy models of solids, liquids, and gases and the concept of latent heat is illustrated in the following graph:

⇒ Thermal energy supplied to a substance that is changing state is used to loosen the intermolecular bonds holding the particles together (completely in the case of a liquid turning into a gas)

⇒ The thermal energy is called latent heat because during the change of state the temperature does not change, despite thermal energy being supplied to the substance

⇒ The value of l_v and l_f for a few materials are seen in the table below:

⇒ Once again, the high values for water mean that a high proportion of the water on planet Earth is in the liquid state, and our ambient temperature is kept within a relatively small range

⇒ Also see our notes on:

• Thermodynamics
• The Gas Laws
• Avogadro's law, the ideal gas equation and moles
• Ideal Gases
• A molecular kinetic theory model
• Comparing two models of the behaviour of gases