Temperature & Heat

Kinetic Molecular Theory Matter is composed of tiny particles – Atoms – Molecules The particles of matter are in constant random motion – Gas: random velocities and collisions – Liquid: particles move and vibrate while remaining in contact with other particles – Solid: particles vibrate in place (their relative positions remain fixed)

Temperature Temperature is a measure of how hot or cold an object is, but what is it in terms of KMT? Temperature is a measure of the average kinetic energy of the particles in a substance – Since every atom or molecule is moving or vibrating, it has kinetic energy – Temperature is a measure of the average kinetic energy that each particle has – Temperature by itself gives no information about how much total energy is present in the substance

Thermal Energy Thermal energy is the total kinetic energy of the particles in a substance – Loosely speaking, thermal energy is “heat energy” We measure thermal energy by keeping track of changes in internal energy, U U = total energy in a system of particles = thermal energy + chemical energy + nuclear energy A change in the thermal energy results in a change in internal energy,  U The unit for internal energy is the joule, J

Heat Heat is the transfer of thermal energy from one object (substance, body) to another due to a temperature difference – Object A loses energy while Object B gains energy Heat is represented by the symbol Q Heat, like thermal energy, has units of joules (J) heat (Q) Object AObject B TATA TBTB T A > T B

Heat & Internal Energy If an object absorbs heat (and no work is done), its internal energy increases Likewise, if an object releases heat (and no work is done), its internal energy decreases U Q U increases  U > 0 U Q U decreases  U < 0

Direction of Heat & Thermal Equilibrium Heat requires a temperature difference Heat flows spontaneously from hotter objects to colder ones (higher temp. to lower temp.) Temperature tells us whether heat transfer can or cannot occur: – Yes it can, if there is a temperature difference – No it can’t, if there is no temperature difference If two objects are at the same temperature, they are in thermal equilibrium – Objects in thermal equilibrium cannot transfer heat

Zeroth Law of Thermodynamics The Zeroth Law of Thermodynamics says: If two bodies are in thermal equilibrium with a third body, they are in thermal equilibrium with each other – The zeroth law ensures that temperature is a useful physical quantity – Without the zeroth law, temperature would not be able to predict heat transfer The physicist James Clerk Maxwell expressed this law as “All heat is of the same kind”

Temperature Measurement A thermometer is a device that measures temperature The classic mercury (or alcohol) thermometer uses two spontaneous processes: – The “bulb” of the thermometer (which contains most of the mercury) is placed in contact with an object and allowed to reach thermal equilibrium with it – Thermal expansion/contraction of the very thin column of mercury above the bulb indicates the temperature in degrees scale bulb column glass

Temperature Scales There are three temperature scales: – Fahrenheit (  F) – Celsius (  C) – Kelvin (K) To convert Celsius to Fahrenheit: T F = (9/5)T C To convert Fahrenheit to Celsius: T C = (5/9)(T F  32.0) To convert Celsius to Kelvin T = T C Water FreezesWater Boils Fahrenheit 32  F212  F Celsius 0C0C100  C Kelvin K K

Comparison of the Temp Scales:

Absolute Zero Absolute zero is the name for the lowest possible temperature For a substance at absolute zero: – the particles cease to move – the thermal energy content is zero – the temperature, in Kelvin, is zero Nothing in the universe is ever at absolute zero – Absolute zero is a theoretical state determined by extrapolation – Scientists have brought very small quantities to temperatures less than 2  K

The Kelvin Scale The Kelvin scale is the scientific temperature scale used in thermodynamics – The kelvin (K) is the unit of temperature – 0 K corresponds to absolute zero – The temperature steps in Kelvin are the same as the steps in Celsius:  T kelvin =  T celsius When measured using the Kelvin scale, temperature becomes a true physical quantity – The thermal energy in a gas (U) is proportional to the temperature in kelvin (T): U  T(true only for kelvin)

Types of Heat Transfer There are three primary types of heat transfer: – Conduction – Convection – Radiation Conduction is heat transfer within an object or between objects when they are touching Convection is when heat is carried from one place to another by a fluid Radiation is heat transfer by electromagnetic radiation (light, infrared, microwaves, etc.)

T1T1 T2T2 H L A Conduction Conduction in a material happens when there is a temperature gradient in the material The rate of heat transfer, H, in watts, is given by H =  Q/  t = kA(T 1  T 2 )/L – k is the thermal conductivity of the material with units of W/(m  C) = W/(m  K) – A is the cross-sectional area (m 2 ), L is the length (m) T 1 > T 2

Example Conduction Problem An aluminum rod of length 30.0 cm and diameter 1.5 cm has a temperature of 85  C at one end and 18  C at the other. What is the rate of heat flow through the rod? k (Al) = 210 W/(m  K) A =  d 2 /4 =  (.015 m) 2 /4 = 1.77  m 2 H = kA(T 1  T 2 )/L = (210 W/m  K)(1.77  m 2 )(85  18  C)/(0.30m) = 8.3 W

Thermal Expansion Most substances expand when heated and contract when cooled The amount of expansion or contraction (  L) depends on the material and is proportional to the change in temperature  T:  L =  L 0  T –  is the linear coefficient of thermal expansion for the material (units of K -1 ) L0L0 L LL

Example Thermal Expansion Problem An aluminum rod of length 30.0 cm and diameter 1.5 cm increases in temperature by 95  C. How much does the length of the rod increase?  (Al) = 23  K -1  L =  L 0  T = (23  K -1 )(30.0 cm)(95 K) = cm = 6.6  m

Specific Heat The specific heat of a substance is the amount of energy required to change the temperature of 1 kg of that substance by 1  C Specific heat is denoted by “c P ” Specific heat has units of J/kg  C Specific heat equation: Q = c P m  T = c P m(T final  T initial ) where Q is energy transferred as heat

Example How much energy must be transferred as heat to raise the temperature of 0.75 kg of water from 18  C to 100  C?  T = 100  C  18  C = 82  C m = 0.75 kg c P = 4186 J/kg  C Q = (4186 J/kg  C)(0.75 kg)(82  C) = J = 260 kJ

Example What is the specific heat of a 75.0-g piece of metal that releases 1850 J of heat while cooling from 98.6  C to 24.3  C? m = kg Q = J  T = 24.3  C – 98.6  C =  C c p = Q/(m·  T) = (-1850 J)/( kg)/(-74.3  C ) = 332 J/(kg·  C)

Table of Specific Heats MaterialSpecific heat J/(kg  C ) aluminum903 brass376 copper385 iron450 zinc388 silver235 lead130 water4186

Calorimetry A calorimeter is a device used to measure the specific heat of a substance A test substance is heated and placed in the water The amount of heat the water absorbs is Q w = c Pw m w  T w The amount of heat the substance releases is Q x = c Px m x  T x But Q x = -Q w So c Px = -Q w /m x  T x