If we assume that the transformer is 100%, derive the formulas for current in the secondary circuit, and the resistor in the secondary circuit, in terms of the primary circuit.

Specific Heat Capacity and Latent Heat

Temperature

• We associate the concept of temperature with how hot or cold an object feels

• Our senses provide us with a qualitative indication of temperature

• Our senses are unreliable for this purpose

• We need a reliable and reproducible method for measuring the relative hotness or coldness of objects

  • We need a technical definition of temperature

Thermal Contact/Equilibrium

• Two objects are in thermal contact with each other if energy can be exchanged between them.

  • Exchanges can be in the form of heat or radiation and are due to a temperature difference

  • Thermal contact does not necessarily imply physical contact

• Thermal equilibrium is a situation in which two objects would not exchange energy by heat or radiation if they were placed in thermal contact

Zeroth Law of Thermodynamics

The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then all three are in thermal equilibrium with each other.

Temperature

• Temperature can be thought of as the property that determines whether an object is in thermal equilibrium with other objects

• Two objects in thermal equilibrium with each other are at the same temperature. If two objects have different temperatures, they are not in thermal equilibrium with each other

Temperature Scales

• Celsius Scale. Temperature of an ice-water mixture is defined as 0º C (freezing point of water)

• Temperature of a water-steam mixture is defined as 100º C (boiling point of water)

• Absolute (Kelvin) Scale. When the pressure of a gas goes to zero, its temperature is –273.15ºC (called absolute zero). The zero point of the Kelvin scale (0 K) is at –273.15º C.

• To convert: T_C = T_K – 273.15

• NOTE: ∆ T_C = ∆ T_K , but T_C ≠ T_K

Heat

Heat is the process or method of thermal energy transfer between a system and its environment due to the temperature difference between them.

The amount of thermal energy (Q) transferred by heat is measured in Joules or calories (cal):

Distinguish between Temperature and Heat

• Temperature depends on the physical state of a material and is a quantitative hotness or coldness.

• In physics, “heat” is energy in transit from one body or system to another because of a temperature difference, never to the amount of energy contained within a particular system.

• We can change the temperature of a body by adding or subtracting heat, or by adding or subtracting energy in other ways, i.e. mechanical work.

Various types of Heat Transfer

Thermal Conduction: transfer of thermal energy from hot to cold objects by the exchange of KE between molecules, atoms, electrons or other particles, e.g. heating a metallic cooking pot on the stove;

Thermal Convection: transfer of thermal energy by movement of substance, e.g. radiators heating your lecture room;

Thermal Radiation: energy transferred continuously by all objects through electromagnetic waves produced by the thermal vibration of their molecules.

Heat Capacity (of an object)

A constant of proportionality between the amount of energy absorbed or lost by an object, by heat, and the resulting temperature change of the object

• The amount of thermal energy (Q) absorbed or lost by an object as its temperature changes from T_i to T_f is:

• C(T) is the heat capacity characteristic to the object

• C is measured in J K^-1

Specific Heat Capacity

• The heat capacity of a substance of mass m is also defined as:

C(T) = m c(T), where c(T) is the specific heat capacity, measured in J kg^-1 K^-1.

• If c does not depend on T, then:

Latent heat

• A substance can be heated without changing its temperature.

• This occurs when the substance changes phase:

• solid to liquid (fusion)

• liquid to gas (vaporisation)

• solid to gas – directly (sublimation)

Latent heat of fusion and vaporisation

• Latent heat of fusion (L_f ) or vaporisation (L_v): the amount of energy added to 1 kg of a substance to change it from solid to liquid or liquid to gas without changing its temperature.

Fusion:

Vaporisation:

both measured in J kg^-1.

Latent Heat and Interatomic Interaction

• U₀ is a measure of the energy needed to separate the molecules (break the interatomic bonds)

• It gives an approximation of the latent heat of a substance

Thermal Expansion of Solids and Liquids

• The thermal expansion of an object is due to changes in the average separation of its atoms and molecules;

• The vibration amplitudes of atoms and molecules are temperature dependent;

• The object expands if the vibration amplitudes increase, and contracts when the amplitudes decrease;

• Practical applications: thermometers, thermostats, bimetal strips, etc.

Linear thermal expansion

• The change in length (ΔL) is proportional to the change in temperature (ΔT) for small ΔT :

• α is the linear coefficient of expansion, depends on material and has units of °C ^-1 ;

• L₀ is the initial length of the object ;

• Large temperature differences can cause thermal stress and containers to break.

Area and volume thermal expansion

The change in area ΔA resulting from a change in temperature ΔT is:

γ = 2α is the area coefficient of expansion (unit of °C^-1) and A₀ is the object’s initial cross-section area.

The change in volume ΔV resulting from a change in temperature ΔT is:

β = 3α is the volume coefficient of expansion (unit of °C^-1) and V₀ is the object’s initial volume.